Wind Energ. Sci., 5, 1623–1644, 2020
https://doi.org/10.5194/wes-5-1623-2020
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.
Changing the rotational direction of a wind turbine under
veering inflow: a parameter study
Antonia Englberger
1
, Julie K. Lundquist
2,3
, and Andreas Dörnbrack
1
1
German Aerospace Center, Institute of Atmospheric Physics, Oberpfaffenhofen, Germany
2
Department of Atmospheric and Oceanic Sciences, University of Colorado Boulder,
Boulder, Colorado, USA
3
National Renewable Energy Laboratory, Golden, Colorado, USA
Correspondence: Antonia Englberger (antonia.englberger@dlr.de)
Received: 17 December 2019 – Discussion started: 28 January 2020
Revised: 25 September 2020 – Accepted: 13 October 2020 – Published: 23 November 2020
Abstract. All current-day wind-turbine blades rotate in clockwise direction as seen from an upstream perspec-
tive. The choice of the rotational direction impacts the wake if the wind profile changes direction with height.
Here, we investigate the respective wakes for veering and backing winds in both hemispheres by means of large-
eddy simulations. We quantify the sensitivity of the wake to the strength of the wind veer, the wind speed,
and the rotational frequency of the rotor in the Northern Hemisphere. A veering wind in combination with
counterclockwise-rotating blades results in a larger streamwise velocity output, a larger spanwise wake width,
and a larger wake deflection angle at the same downwind distance in comparison to a clockwise-rotating turbine
in the Northern Hemisphere. In the Southern Hemisphere, the same wake characteristics occur if the turbine
rotates counterclockwise. These downwind differences in the wake result from the amplification or weakening
or reversion of the spanwise wind component due to the effect of the superimposed vortex of the rotor rotation
on the inflow’s shear. An increase in the directional shear or the rotational frequency of the rotor under veering
wind conditions increases the difference in the spanwise wake width and the wake deflection angle between
clockwise- and counterclockwise-rotating actuators, whereas the wind speed lacks a significant impact.
Copyright statement. The copyright of the authors Antonia En-
glberger and Andreas Dörnbrack for this publication are transferred
to Deutsches Zentrum für Luft- und Raumfahrt e. V., the German
Aerospace Center. This work was authored (in part) by the National
Renewable Energy Laboratory, operated by Alliance for Sustain-
able Energy, LLC, for the US Department of Energy (DOE) under
contract no. DE-AC36-08GO28308. Funding provided by the US
Department of Energy Office of Energy Efficiency and Renewable
Energy Wind Energy Technologies Office. The views expressed in
the article do not necessarily represent the views of the DOE or the
US Government. The US Government retains and the publisher, by
accepting the article for publication, acknowledges that the US Gov-
ernment retains a nonexclusive, paid-up, irrevocable, worldwide li-
cense to publish or reproduce the published form of this work, or
allows others to do so, for US Government purposes.
1 Introduction
Most modern industrial-scale wind turbines rotate clockwise,
as seen from a viewer looking downwind. Traditional Danish
windmills turned counterclockwise (Maegaard et al., 2013),
as they were built by right-handed millers who preferred
the thin end of the laths to be pointing towards the left
on the blades. This rotational direction was adapted by the
wind-turbine pioneer Christian Riisager and subsequently
by the company Tvind. In 1978, Erik Grove-Nielsen de-
signed the first 5 m fiberglass blades. He and his wife Tove
chose a clockwise rotational direction of the blades to distin-
guish their product from Tvind. Descendants of the Riisager
wind turbine (Windmatic and Tellus) rotate counterclock-
wise, while those of Grove-Nielsen (Vestas, Bonus – now
Siemens, Nordtank, and Enercon) rotate clockwise. Three
Published by Copernicus Publications on behalf of the European Academy of Wind Energy e.V.
1624 A. Englberger et al.: Changing the rotational direction of a wind turbine under veering inflow
of the four clockwise-rotating blade manufacturers became
market leaders in the international wind power industry, and
the clockwise-rotating blades, eventually, became the global
standard (Maegaard et al., 2013). The clockwise blade rota-
tion is, therefore, a historical coincidence without physical
motivation.
Rotating blades encounter a variety of wind conditions.
In a convective regime during the daytime above the surface
layer, there is no significant change in the incoming wind
direction or wind speed with height and the inflow condi-
tions are uniform over the whole rotor area. A nocturnal sta-
bly stratified regime, however, often generates wind profiles
with changing magnitude (vertical wind shear) and direction
(wind veer; Lindvall and Svensson, 2019). Vertical varia-
tions in both quantities reflect the balance between Coriolis
force and friction. Friction affects the lowest part of the wind
profile and contributes as internal friction in the flow while
the rotational direction of the wind vector in the Ekman spi-
ral aloft depends on the hemisphere. In the Northern Hemi-
sphere (NH; Southern Hemisphere, SH), winds tend to ro-
tate clockwise (counterclockwise) with height (Stull, 1988).
Veer occurs on many nights both onshore (Walter et al.,
2009; Rhodes and Lundquist, 2013; Sanchez Gomez and
Lundquist, 2020) and offshore (Bodini et al., 2020, 2019).
According to 2 years of meteorological tower measurements
in Lubbock (Texas; Walter et al., 2009) and 3 months of
lidar observations in north-central Iowa (Sanchez Gomez
and Lundquist, 2020), veer occurs in well over 70 % of
those stable boundary layer (SBL) occurrences (≈ 76 % in
Walter et al., 2009, and ≈ 78 % in Sanchez Gomez and
Lundquist, 2020). In the remaining 22 % (Sanchez Gomez
and Lundquist, 2020) to 24 % (Walter et al., 2009), a backing
wind occurs. A backing wind is characterized by a counter-
clockwise wind direction change with height in the NH.
The frequency of occurrence of a veering wind depends
on many criteria. A wind direction change with height oc-
curs mainly at night. Secondly, seasonal differences occur.
Thirdly, the frequency of occurrence of veering or backing is
location specific. In Lubbock (Texas; Walter et al., 2009) and
in north-central Iowa (Sanchez Gomez and Lundquist, 2020),
a veering wind occurs on three out of four nights. In their
global climatology of veer based on radiosonde data, Lind-
vall and Svensson (2019) find stronger veer (or backing for
the SH) in midlatitudes (see their Fig. 3). Of course, topog-
raphy can change the frequency of occurrence significantly.
Each location has its own percentage values of the occur-
rence of a veering wind. In this study, a directional shear of
0.08
◦
m
−1
is applied in the reference case, as it corresponds
to the mean of the frequency of occurrence of a veering in-
flow in Walter et al. (2009). Further, seasonal dependence
occurs (Bodini et al., 2019, 2020). The longer-lasting nights
during winter are characterized by smaller mean values of
the directional shear (minimum winter values in December
of 0.03
◦
m
−1
, according to 13 months of offshore lidar mea-
surements in Massachusetts; Bodini et al., 2020, Fig. 4).
The shorter nights during summer, however, are character-
ized by larger mean values of the directional shear (maxi-
mum summer values in June of 0.095
◦
m
−1
; Bodini et al.,
2020, Fig. 4). The occurrence of a specific directional shear
(e.g., ds = 0.08
◦
m
−1
) for a specific wind speed (between 9
and 11 m s
−1
, similar to the reference case used here) is much
larger during winter (85 % of the veering cases are character-
ized by ds ≤ 0.08
◦
m
−1
) in comparison to the summer (45 %;
Bodini et al., 2020, Fig. 5).
The wind turbine’s wake characteristics in a veering wind
regime differ for counterclockwise- and clockwise-rotating
blades (Englberger et al., 2020). The induced vortex compo-
nent of the near wake’s flow is determined by the rotation of
the blades. The wake rotates opposite to the blade rotation
due to aerodynamics and design of the wind-turbine blades
(Zhang et al., 2012). In contrast, the rotational direction of
the far wake is determined by the Ekman spiral. If a northern
hemispheric Ekman spiral interacts with clockwise-rotating
blades, the spanwise flow component in the wake weakens
or even reverses due to a superposition with the vortex of the
near wake and attenuates to the inflow in the far wake. In this
case, the near wake’s counterclockwise rotation diminishes
and becomes clockwise. After this reversion or likewise in
the case of a reduction in the spanwise wake component, the
wake’s rotation strength intensifies downwind. Conversely,
if the same inflow interacts with counterclockwise-rotating
blades, the spanwise flow component is amplified in the near
wake, because the rotational direction persists in the whole
wake and the wake’s rotation strength weakens downwind.
The modification of the spanwise flow component also im-
pacts the streamwise velocity in the wake. It affects the ve-
locity deficit in the near wake, the streamwise wake elon-
gation of the wake, the spanwise wake width, and the de-
flection angle of the wake (Englberger et al., 2020). There
also exists a rotational-direction impact on the streamwise
velocity component in a flow regime without wind veer (Ver-
meer et al., 2003; Shen et al., 2007; Sanderse, 2009; Kumar
et al., 2013; Hu et al., 2013; Yuan et al., 2014; Mühle et al.,
2017). Vasel-Be-Hagh and Archer (2017) simulated a wind
farm similar to Lillgrund in Sweden with alternative rota-
tional direction of the rotors, starting with clockwise in the
first row. Including wind shear but no wind veer in the in-
flow conditions, the power output was 1.4 % larger in com-
parison to only clockwise-rotating rotors in the wind farm.
However, compared to the wake differences for clockwise-
and counterclockwise-rotating rotors in a flow regime with
wind veer, the differences are small in the case of no wind
veer (Englberger et al., 2020). Therefore, the 1.4 % in Vasel-
Be-Hagh and Archer (2017) can be considered a lower limit;
the consideration of veer amplifies this difference.
In this study, we investigate the relationship between the
upstream wind profile and the direction of the turbine rota-
tion using large-eddy simulations (LESs). Both clockwise-
and counterclockwise-rotating actuators are embedded in a
veering as well as a backing inflow for both hemispheres.
Wind Energ. Sci., 5, 1623–1644, 2020 https://doi.org/10.5194/wes-5-1623-2020
A. Englberger et al.: Changing the rotational direction of a wind turbine under veering inflow 1625
In the case of a veering inflow in the NH, we carry out a
parameter study investigating the impact of the magnitude of
the geostrophic wind, the directional shear, and the rotational
frequency of the rotor. The results of the rotational-direction
impact on the wake are interpreted for all simulations with a
theoretical analysis considering a Rankine vortex representa-
tion of the wake. To our knowledge, this is the first parameter
study which investigates the interactions of wake rotational
direction in combination with an Ekman spiral.
Our previous study (Englberger et al., 2020) lays the
groundwork for this investigation, describing in detail the
rotational-direction impact in a stably stratified regime under
veered inflow conditions and in an evening boundary layer
regime under nonveered conditions (in the Northern Hemi-
sphere). Further, that work explains the physical mechanism
responsible for the rotational-direction impact of the blades
on the wake by simple analysis of a linear superposition of
the veering inflow wind field with a Rankine vortex.
This paper is organized as follows. The numerical model
EULAG, the wind-turbine simulation setup, and the metrics
applied in this work are described in Sect. 2. The analysis
predictions are introduced in Sect. 3. The corresponding ide-
alized simulations investigating the rotational-direction im-
pact on the wake follow in Sect. 4. A comparison of the sim-
ulation results to the analysis predictions is given in Sect. 5,
and a conclusion follows in Sect. 6.
2 Numerical model framework
2.1 The numerical model EULAG
The wind-turbine simulations, with prescribed wind and tur-
bulence conditions, are conducted with the flow solver EU-
LAG (Prusa et al., 2008). For a comprehensive description
and discussion of EULAG we refer to Smolarkiewicz and
Margolin (1998) and Prusa et al. (2008).
The Boussinesq equations for a flow with constant density
ρ
0
= 1.1 kg m
−3
are solved for the Cartesian velocity compo-
nents u, v, and w and for the potential-temperature perturba-
tions 2
0
= 2 − 2
e
(Smolarkiewicz et al., 2007):
dv
dt
= −∇
p
0
ρ
0
+ g
2
0
2
0
+ V + β
v
F
WT
ρ
0
, (1)
d2
0
dt
= H − v∇2
f
, (2)
∇ · (ρ
0
v) = 0, (3)
with 2
e
representing the environmental or background state
and 2
0
representing the constant reference value of 300 K. In
Eqs. (1)–(3), d/dt , ∇ and ∇ · represent the total derivative,
the gradient, and the divergence, respectively. The quantity
p
0
represents the pressure perturbation with respect to the
environmental state. Further, g represents the vector of ac-
celeration due to gravity. The subgrid-scale terms V and H
symbolize viscous dissipation of momentum and diffusion of
heat. F
WT
corresponds to the turbine-induced force and β
v
to the rotational direction. All following simulations are per-
formed without an explicit subgrid-scale closure as implicit
LESs (Grinstein et al., 2007), to remove any question of the
influence of the subgrid-scale closure on the results. Further,
we apply a free-slip vertical boundary condition.
The turbine-induced forces (F
WT
) in Eq. (1) are
parametrized with the blade element momentum (BEM)
method as the actuator disc, including a nacelle and ex-
cluding the tower. The BEM method enables the calcula-
tion of the steady loads, thrust, and power for different wind
speeds and rotational speeds of the blades. The airfoil data
of the 10 MW reference wind turbine from DTU (Bak et al.,
2013) are applied, whereas the radius of the rotor as well
as the chord length of the blades is scaled to a rotor with
a diameter of 100 m. For a more detailed description of the
wind-turbine parametrization and all values used in the wind-
turbine parametrization, we refer to parametrization B of En-
glberger and Dörnbrack (2017).
The actuator disc rotates in a clockwise or counterclock-
wise direction, depending on the choice of β
v
∈{−1, 1}.
The rotor rotation is not directly simulated; instead, the
rotor forces are exerted directly on the velocity fields in
Eq. (1). A clockwise-rotating rotor initiates a counterclock-
wise wake rotation and vice versa, following conservation
of angular momentum (Zhang et al., 2012). In this work, a
common clockwise rotor rotation “cr” is defined as β
v
= 1
and β
w
= −1 and a counterclockwise rotor rotation “ccr” as
β
v
= −1 and β
w
= 1, with β
u
= 1 in both cases.
2.2 Setup of the wind-turbine simulations
Wind-turbine simulations on 512 × 64 × 64 grid points with
a horizontal and vertical resolution of 5 m and open bound-
aries are performed for veering and nonveering inflow last-
ing 40 min. The rotor of the wind turbine has a diameter D
as well as a hub height z
h
of 100 m and is located at 300 m
downwind from the inflow boundary and centered in the
spanwise y direction.
A veering wind profile can be described by the Ekman spi-
ral:
u
Ekman
(z) = u
g
·
(
1 − exp
(
−zγ
)
cos(zγ )
)
, (4)
v
Ekman
(z) = u
g
·
(
exp
(
−zγ
)
sin(zγ )
)
, (5)
following Stull (1988), with a geostrophic wind u
g
and
γ =
r
f
2κ
representing a Coriolis parameter f = 1.0 × 10
−4
s
−1
and an
eddy viscosity coefficient κ.
Wind direction change between two heights is defined as
directional shear. As we assume the directional shear to be an
impact factor for the interaction process of a rotating system
with veering inflow, a modified version of the Ekman spiral
https://doi.org/10.5194/wes-5-1623-2020 Wind Energ. Sci., 5, 1623–1644, 2020
1626 A. Englberger et al.: Changing the rotational direction of a wind turbine under veering inflow
is applied as v
f
in the simulations in this work. Further, the
negative vertical gradient of the streamwise velocity in the
supergeostrophic component of the Ekman spiral is not con-
sidered in u
f
.
The simulations are initialized with the streamwise veloc-
ity profile
u
f
(z) = u
g
·
(
1 − exp
(
−zγ
))
, (6)
with an eddy viscosity coefficient κ = 0.06 m
2
s
−1
. The cor-
responding spanwise velocity profile is
v
f
(z) = 0 (7)
in the case of no veering inflow with
∂v
f
∂z
= 0 and
v
f
(z) = u
f
(z) · tan(φ
wind
(z)) (8)
in the case of veering inflow with
∂v
f
∂z
6= 0, with a given di-
rectional shear
ds =
1φ
100 m
, (9)
with 1φ = φ
150 m
− φ
50 m
and
φ(z) = ±21φ
1 −
z
D
(10)
in the lowest 200 m and constant above. The influence of the
Coriolis force on the flow field is only included in the sim-
ulations via Eqs. (6) and (8). Note that no Coriolis force is
applied in the numerical model (Eq. 1).
For u
f
and v
f
, we consider the NH (f > 0) and the SH
(f < 0) and a veering (1φ > 0 in NH; 1φ < 0 in SH) and a
backing (1φ < 0 in NH; 1φ > 0 in SH) wind. In the refer-
ence simulation (with a veering wind in the NH), the direc-
tional shear is 0.08
◦
m
−1
with v
f
(z
h
) = 0. The initial vertical
velocity is
w
f
(z) = 0 (11)
in all simulations. The flow components u
f
, v
f
, and w
f
are
used for specifying the initial conditions. The pressure solver
in EULAG further applies u
f
and v
f
as boundary conditions.
The potential temperature is
2
e
(z) = 2
0
+
3 K
200 m
z (12)
in the lowest 200 m and 303 K above.
For a veering wind in the NH, we modify the geostrophic
wind, the directional shear, and the rotational frequency of
the rotor. We sample winds with a geostrophic wind compo-
nent of u
g
= 6 m s
−1
, u
g
= 10 m s
−1
(reference simulation),
and u
g
= 14 m s
−1
, the first and last of which are referred to
with the acronyms u6 and u14 in the simulation nomencla-
ture. Further, we apply a directional shear of 0.04, 0.08, 0.12,
0.16, and 0.20
◦
m
−1
corresponding to weak (ds4), moder-
ate (reference simulation), moderate to strong (ds12), strong
(ds16), and very strong (ds20) shear. As an additional pa-
rameter, the rotational frequency ranges from = 0.058 s
−1
,
= 0.12 s
−1
, and = 0.175 s
−1
to = 0.23 s
−1
, corre-
sponding to low (l), moderate (reference simulation), high
(h), and very high (vh) in the simulation nomenclature.
This work is a parameter study investigating the impacts
of the inflow (directional shear, wind speed) and the rotating
system (rotational frequency) on the wake. The wake’s im-
pact by the rotational direction of the rotor depends on the
mean wind profile, which is determined by the geostrophic
wind (Eqs. 6 and 8) and the directional shear (Eq. 9). Tur-
bulence modifies the strength of the wakes but not the oc-
currence (Appendix and Sect. 5). Therefore, we perform
the simulations as implicit LESs with no explicit subgrid-
scale closure model. Moreover, we apply the turbulence
parametrization by Englberger and Dörnbrack (2018b) to
perturb the flow field during the numerical integration. This
turbulence parametrization provides a computationally fast
method for wind-turbine simulations with open horizontal
boundary conditions in a small domain. It includes stability-
dependent atmospheric characteristics in the inflow. This
makes the method very suitable for parameter studies. We
superimpose upon the inflow wind field turbulent fluctua-
tions in a neutral boundary layer precursor simulation (En-
glberger and Dörnbrack, 2017), as represented by the term I
in Eq. (13), where u
p
i
∗
,j,k
is the velocity vector of a neutral
boundary layer equilibrium state at each grid point i, j , and
k.
u
∗
p
δ
i=1,j,k
= α
0
· α
i
∗
,j,k
·
u
p
i
∗
,j,k
−
1
n · m
n
X
i=1
m
X
j=1
u
p
i,j,k
!
| {z }
I
(13)
The indices of the grid points are denoted by i = 1 . . . n, j = 1
.. . m, and k = 1 . . . l in the x, y, and z directions, respec-
tively. The star refers to a streamwise shift by one grid point
at every time step δ with i
∗
= i +δ, whereas i
∗
= [1, n] and δ
∗
represents the passed number of time steps. The prefactor α
0
represents the amplitude of the turbulence perturbations and
α
i
∗
,j,k
represents adjustable stratification-dependent param-
eters for convective and stable regimes as well as the transi-
tions between them. The stratification-dependent parameters
were retrieved from a 30 h diurnal-cycle simulation from En-
glberger and Dörnbrack (2018a).
In the following simulations we apply nighttime represen-
tations using values of α = 0.3, α
u
= 0.15, α
v
= 0.24, and
α
w
= 0.13 (Englberger and Dörnbrack, 2018b, Table 1). A
rather similar setup including the turbulence parametrization
has been applied in Englberger and Lundquist (2020).
Wind Energ. Sci., 5, 1623–1644, 2020 https://doi.org/10.5194/wes-5-1623-2020
A. Englberger et al.: Changing the rotational direction of a wind turbine under veering inflow 1627
Figure 1. Schematic illustration of the top sector and the bottom
sector, as well as the left and right sectors, defined from a view
looking downwind towards the wind turbine on the disc.
2.3 Metrics
For the investigation of the rotational-direction impact
on the wake, the following characteristics are calculated
from the simulation results: the spatial distribution of the
time-averaged discrete streamwise velocity u
i,j,k
, the time-
averaged discrete spanwise velocity v
i,j,k
, and the stream-
wise velocity deficit
VD
i,j,k
≡
u
1,j,k
− u
i,j,k
u
1,j,k
. (14)
The characteristics are averaged over the last 30 min of the
40 min wind-turbine simulation. The 30 min temporal aver-
age is calculated online in the numerical model according to
the method of Fröhlich (2006, Eq. 9.1).
In the following, the quantities u
i,j,k
and v
i,j,k
are eval-
uated and discussed for top and bottom sectors. They result
from a division of the rotor area into four sections of 90
◦
, as
shown in Fig. 1, including all grid points with a distance r
from the rotor center 0 m < r ≤ R. The left and right sectors
are defined from a view looking downwind towards the wind
turbine on the disc.
3 Theoretical analysis
In this section, we construct a simple analytical model of
the interaction of the rotating wake of a wind turbine with
a sheared ambient flow. The rotating wake is prescribed by
a Rankine vortex, whereas the ambient flow is described
by three different inflow conditions (no veer, veering wind,
backing wind). In the case of a veering inflow, the relations
are also evaluated for three different parameters (wind speed,
directional shear, rotational velocity). The approach follows
Englberger et al. (2020) and is modified to allow different
directional-shear values.
A rotating system can be described by a Rankine vortex
with the radial dependence r, the rotational velocity ω, and
the angle ϑ in a y–z plane:
v
v
(z) = ±ωr sin(ϑ), (15)
w
v
(z) = ∓ωr cos(ϑ). (16)
The veering inflow is described by Eqs. (4) and (5),
whereas no wind veer is described by Eq. (7). In this analysis
we apply the simplified Eqs. (6) and (8) for the veering in-
flow, as they allow a variety of directional-shear values. Both
inflow cases result in a superposition of the spanwise com-
ponents v
f
(Eqs. 7 and 8) and v
v
(Eq. 15) in Eq. (17):
v(z, x
down
) =
no veer: v
v
· (1 −
x
down
x
ζ
)
= ±ωr sin(ϑ)(1 −
x
down
x
ζ
)
veer: v
f
+ v
v
· (1 −
x
down
x
ζ
)
= u
g
· exp
(
−zγ
)
· tan
21φ
1 −
z
D
±ωr sin(ϑ)(1 −
x
down
x
ζ
)
x
WT
≤ x
down
≤ x
ξ
.
(17)
In Eq. (17), a linear decrease in v
v
(z, x
down
) is assumed for
a given downwind distance x
down
from the rotating system
x
WT
up to x
ξ
with v(z, x
ξ
) = 0. In this work, we only consider
the spanwise flow component, as w
f
= 0 (Eq. 11).
Figure 2 represents the spanwise velocity component v re-
sulting from Eq. (17) at z = 125 m and at z = 75 m at the rotor
center in a lateral direction. The rotating system has a rotor
center z
h
= 100 m and a rotor radius R = 50 m. The vertical
positions are centered in the top and the bottom sectors of
Fig. 1.
The wake resulting from a clockwise (cr) or counterclock-
wise (ccr) rotating rotor interacting with no wind veer are
represented in Fig. 2b. Following Eq. (17), the rotational di-
rection of the rotor determines the sign of v(z, x
down
). There-
fore, the spanwise velocity component has the opposite sign
in the top and the bottom rotor part of both cr and ccr in
Fig. 2b. Approaching x
ξ
, v(z, x
ξ
) = v
f
(z) = 0.
In the case of veering inflow, however, the spanwise flow
component impacts the wake (Eq. 17). The spanwise flow
component results from the Ekman spiral, which is hemi-
spheric dependent. In the NH, f > 0, and, therefore, the
spanwise flow component v
f
(z
h
− R/2) > 0 in the lower ro-
tor half and v
f
(z
h
+ R/2) < 0 in the upper rotor half with
v
f
(z
h
) = 0 (Eq. 8). This situation corresponds to a flow from
right to left in the lower rotor half and from left to right in
the upper rotor half, looking from upwind towards downwind
(Fig. 1). If “+” is applied in Eq. (17), v
v
(z
h
− R/2, x
down
) =
+ωr sin(270
◦
) = −ωr < 0 in the lower rotor half and v
v
(z
h
+
R/2,x
down
) = +ωr sin(90
◦
) = ωr > 0 in the upper rotor
half. However, if “−” is applied in Eq. (17), v
v
(z
h
−
R/2,x
down
) = −ωr sin(270
◦
) = ωr > 0 in the lower rotor
https://doi.org/10.5194/wes-5-1623-2020 Wind Energ. Sci., 5, 1623–1644, 2020
1628 A. Englberger et al.: Changing the rotational direction of a wind turbine under veering inflow
Figure 2. Representations of v(z = 75 m, x
down
) at the rotor cen-
ter in lateral position as bottom and v(z = 125 m, x
down
) as top
(Eq. 17) for a clockwise-rotating (cr) and a counterclockwise-
rotating (ccr) rotor in the case of no veer in (b), a veering wind
in (e), and a backing wind in (h). In the case of a veering wind
in (e), moderate parameters of u
g
= 10 m s
−1
, ds = 0.08
◦
m
−1
, and
ω = 0.12
◦
s
−1
are applied. In the left (a, d, g) and right (c, f, i)
column, only one parameter is changed compared to the veering-
wind situation in (e). Applying low parameters, u
g
= 6 m s
−1
in (a),
ds = 0.04
◦
m
−1
in (d), and ω = 0.058
◦
s
−1
in (g), and applying
high parameters, u
g
= 14 m s
−1
in (c), ds = 0.12
◦
m
−1
in (f), and
ω = 0.175
◦
s
−1
in (i).
half and v
v
(z
h
+ R/2, x
down
) = −ωr sin(90
◦
) = −ωr < 0 in
the upper rotor half. The sign “+” corresponds to a counter-
clockwise wake rotation which arises from a clockwise rotor
rotation (Zhang et al., 2012), whereas the sign “−” corre-
sponds to a clockwise wake rotation arising from a counter-
clockwise rotor rotation ccr.
In the case of a clockwise-rotating rotor, the rotor com-
petes against the veer effect with v
v
(z
h
− R/2,x
down
) < 0 su-
perpositioning v
f
(z
h
−R/2) > 0 and v
v
(z
h
+R/2,x
down
) > 0
superpositioning v
f
(z
h
+ R/2) < 0. In both the top and bot-
tom half of the rotor, the spanwise component of the inflow
v
f
is weakened by the vortex component v
v
or even reversed
if | v
v
| > | v
f
|. Approaching downwind, the impact of v
v
decreases and v(z, x
down
) approaches v
f
(z) at x
down
= x
ξ
with v
v
(z, x
ξ
) = 0.
In the case of a counterclockwise-rotating rotor, the wake
vortex intensifies the inflow with v
v
(z
h
− R/2, x
down
) > 0 su-
perpositioning v
f
(z
h
−R/2) > 0 and v
v
(z
h
+R/2,x
down
) < 0
superpositioning v
f
(z
h
+R/2) < 0. The vortex intensifies the
inflow v
f
(z
h
) at all rotor heights. Approaching downwind,
the impact of v
v
decreases and v(z,x
down
) approaches v
f
(z)
at x
down
= x
ξ
with v
v
(z, x
ξ
) = 0. At x
down
= x
ξ
, the situation
is independent of the vortex and the wake has completely re-
covered.
The different behavior of the spanwise wake component is
presented in Fig. 2e. In the case of cr, the vortex component
weakens the spanwise inflow component, resulting in a rever-
sion of the sign of v(z, x
down
) behind the rotor at x
down
< x
ξ
.
In the case of ccr, however, the vortex component intensi-
fies the spanwise inflow component. At x
ξ
, both rotational
directions show the same result, approaching the inflow con-
ditions.
Figure 2h represents the situation for a backing wind.
Only φ(z) (Eq. 10) and, therefore, the flow component v
f
(z)
(Eq. 8) change sign in both the top and bottom half of the
rotor. The vortex component v
v
(z ± R/2, x
down
) is not inflow
dependent. Therefore, the wake behavior of ccr (cr) in the
case of backing wind is comparable to cr (ccr) under veering
inflow, resulting in a decrease (intensification) of v
f
(z) in the
wake, following Eq. (17) with a “−” in Eq. (10).
This analysis shows a rotational-direction-dependent
downwind behavior of the spanwise flow component in the
case of
∂v
f
∂z
6= 0. The superposition of the Rankine vor-
tex with a veering inflow (and likewise the backing wind)
has three impacts. The veering inflow is determined by the
geostrophic wind u
g
and the directional shear ds over the ro-
tor height. The vortex component is determined by the rota-
tional velocity ω of the rotor. The impact of u
g
, ds, and ω
on the expected mean behavior of the spanwise wake com-
ponent is presented in Fig. 2 for low values of the parameters
in the left column (panels a, d, g) and high values in the right
column (panels c, f, i), whereas Fig. 2e represents the veering
case for moderate parameter values.
A decrease in u
g
(Fig. 2a) or ds (Fig. 2d) and like-
wise an increase in u
g
(Fig. 2c) or ds (Fig. 2f) impacts the
mean value of the spanwise wake field. When decreasing
the atmospheric parameter values (Fig. 2a and d), the val-
ues of v
f
(z
h
± R/2) also decrease, leading to a downwind
shift in the sign-changing point of v(z, x
down
) = 0 (compare
Fig. 2a, d to Fig. 2e). A further decrease in v
f
(z ± R/2) ap-
proaching v
f
(z ± R/2) = 0 of the nonveering inflow case re-
sults in Fig. 2b. An increase in u
g
(Fig. 2c) or ds (Fig. 2f)
results in an increase in v
f
(z ± R/2) and an upward shift in
the sign-changing point. If the atmospheric parameter values
increase (decrease), the difference in the slope of the span-
wise component between cr and ccr also increases (Fig. 2c
and f; decreases in Fig. 2a and d). Likewise, the slope in the
case of cr increases for high values (Fig. 2c and f in compar-
ison to low values Fig. 2a and d), whereas in the case of ccr,
the slope decreases for larger values of the inflow parameters
(Fig. 2c and f vs. Fig. 2e vs. Fig. 2a and d). This behavior can
be interpreted as an increase in the difference in the wake be-
tween cr and ccr if the atmospheric parameters increase.
Wind Energ. Sci., 5, 1623–1644, 2020 https://doi.org/10.5194/wes-5-1623-2020
A. Englberger et al.: Changing the rotational direction of a wind turbine under veering inflow 1629
Figure 3. y–z cross sections for veering and no veering (NV) inflow
simulations at x = 3 D for CR (first column), CCR (second column),
CR_NV (third column), and CCR_NV (last column). The first row
(a–d) presents the (v, w) vectors in the y–z plane; the second row
(e–h) presents the spanwise wake velocity v; and the third row (i–
j) presents the vertical wake velocity w. The blue circle represents
the circumference of the actuator disc. This picture is looking from
upwind towards downwind on the wake (Fig. 1, corresponding to
the left sector for y < 0 D and the right sector for y > 0 D).
The rotational velocity ω controls the magnitude of the
spanwise vortex component. A decrease in ω (Fig. 2g) and
likewise an increase (Fig. 2i) also influence the mean value
of the spanwise wake field, especially in the near wake. A
decrease in ω decreases v(z,x
down
) directly behind the ro-
tor (Fig. 2g), whereas an increase results in an increase in
v(z, x
down
) in the near wake (Fig. 2i). Larger values of ω lead
to a less rapid wake recovery in the near wake.
As a veering wind in the NH is comparable to a backing
wind in the SH (following the definition via Eq. 10), all pan-
els in Fig. 2 are also valid for the SH with red lines repre-
senting ccr_SH, blue lines representing cr_SH, dashed lines
referring to the top rotor part, and solid lines referring to the
bottom rotor part.
4 Idealized simulations – rotational-direction impact
on the wake
4.1 Veering vs. no veering inflow
The analysis of the preceding section predicts a rotational-
direction impact on the spanwise velocity component v (and
likewise the vertical component w) in the wake under veering
(or backing) inflow, whereas the wake characteristics in the
case of no veer are independent of the rotational direction of
the rotor. This rotational-direction impact is investigated by
LESs with veering and no veering inflow, with the simula-
tion CR, CCR, CR_NV, and CCR_NV conducted with the
parameters as listed in Table 1. The interactions between the
wake rotation and the inflow are embodied in Fig. 3 in the
cross stream and vertical velocities at x = 3 D. The first two
columns represent CR and CCR in the case of veering in-
flow, whereas the last two columns correspond to no wind
veer in the incoming flow field. The top row (Fig. 3a–d) rep-
resents the vectors (v, w). The evolution of v and w is repre-
sented in the second row (Fig. 3e–h) for v and in the third row
(Fig. 3i–l) for w. In the case of no wind veer, the sign of v
is opposite in the upper and the lower rotor half for CR_NV
and CCR_NV (Fig. 3g and h), as predicted by the analysis
(Eq. 17). The same is valid for the sign of w (Fig. 3k and l).
The numerical model shows a clockwise-rotating wake in
the case of CCR_NV (while looking from upwind towards
downwind; Fig. 1) and a counterclockwise-rotating wake in
the case of CR_NV.
Under veering inflow, the simulated wake rotates clock-
wise in the case of CCR (Fig. 3b) and counterclockwise in
the case of CR (Fig. 3a), similar to the no-veer case (Fig. 3d
and c). However, in comparison to the no-veer case, the
strength of rotation differs and is much more pronounced in
the case of CCR (Fig. 3b) in comparison to CR (Fig. 3a).
This rotation arises from the spanwise velocity component,
as the vertical velocity (Fig. 3i and j) is comparable to the
nonveering cases (Fig. 3k and l). The positive and negative
perturbations in v have the same positive and negative pat-
terns in CR (Fig. 3e vs. Fig. 3g) and CCR (Fig. 3f vs. Fig. 3h)
as in CR_NV and CCR_NV in the corresponding rotor sec-
tor at x = 3 D, although with smaller | v | values in the upper
and lower rotor sector in the case of CR and larger | v | val-
ues in the case of CCR. This simulated amplification of the
spanwise flow component in the case of CCR (Fig 3f) and
weakening up to a reversion of the sign in the wake region at
x = 3 D in the case of CR (Fig. 3e) is in agreement with the
predictions of the analysis (Eq. 17) and Fig. 2.
A downwind distance of x = 3 D is visualized in Fig. 3
because a significant spanwise vortex impact on the span-
wise flow component in the wake can be expected. In the
following, special emphasis is placed at x = 7 D, which is
often considered a typical downwind distance for a hypo-
thetical waked wind turbine in numerical simulation stud-
ies (e.g., Gaumond et al., 2014; Abkar et al., 2016). At
x = 7 D, the vortex impact is much smaller compared to
x = 3 D (Fig. 3), resulting in an increase in the impact of the
atmospheric flow.
As the rotational direction has a significant impact on the
spanwise flow component at x = 3 D (Fig. 3), an impact on
the streamwise flow component is also expected. The nu-
merical results for the streamwise velocity component are
presented for veering (CR, CCR) and nonveering (CR_NV,
CCR_NV) inflow by x–y cross sections of the streamwise
velocity in the top half of the rotor disc at z = 125 m (Fig. 4a–
d), at hub height at z = 100 m (Fig. 4e–h), and in the bottom
half of the rotor disc at z = 75 m (Fig. 4i–l).
The effect of wind veer on the streamwise velocity com-
ponent of clockwise-rotating wind turbines is investigated by
comparing CR to CR_NV, in Fig. 4a vs. Fig. 4c at z = 125 m,
Fig. 4e vs. Fig. 4g at z = 100 m, and Fig. 4i vs. Fig. 4k at
z = 75 m. Inflow veer causes a more rapid wake recovery at
all heights, based on comparison of the velocity deficit con-
https://doi.org/10.5194/wes-5-1623-2020 Wind Energ. Sci., 5, 1623–1644, 2020
1630 A. Englberger et al.: Changing the rotational direction of a wind turbine under veering inflow
Table 1. List of all performed simulations in this study for a clockwise (leftmost column) and a counterclockwise (rightmost column) rotor
rotation. The parameters u
g
, ds, and refer to both rotational directions, whereas the only difference e.g., between CR and CCR in the
first line is the rotational direction. Further, _NV represents no wind veer and _b a backing wind, _ds refers to varying the directional shear,
_u refers to varying the geostrophic wind, and _ refers to varying the rotational frequency in the corresponding simulations.
Simulations with different rotational directions of the rotor
Clockwise u
g
(m s
−1
) ds (
◦
m
−1
) (s
−1
) Counterclockwise
CR 10 0.08 0.12 CCR
CR_NV 10 0 0.12 CCR_NV
CR_b 10 −0.08 0.12 CCR_b
CR_ds4 10 0.04 0.12 CCR_ds4
CR_ds12 10 0.12 0.12 CCR_ds12
CR_ds16 10 0.16 0.12 CCR_ds16
CR_ds20 10 0.20 0.12 CCR_ds20
CR_u6 6 0.08 0.12 CCR_u6
CR_u14 14 0.08 0.12 CCR_u14
CR_l 10 0.08 0.058 CCR_l
CR_h 10 0.08 0.175 CCR_h
CR_vh 10 0.08 0.23 CCR_vh
tours. Because enhanced
∂v
f
∂z
6= 0 in the case of veering wind,
it provides a source of resolved turbulence resulting in higher
entrainment in comparison to the no-veer case. Further, in-
flow wind veer causes wake deflection in relation to a ver-
tical plan through the nacelle at y = 0 in both the top half
(Fig. 4a vs. Fig. 4c) and the bottom half (Fig. 4i vs. Fig. 4k)
of the rotor disc. The wake in the veered simulation CR
is deflected towards the right (y > 0 D; towards the left is
y < 0 D) in the upper (lower) rotor part (Fig. 4a and i). In
the nonveered simulation CR_NV, the wake is only slightly
deflected towards the left in the top-tip sector (Fig. 4c) and
towards the right in the bottom-tip sector (Fig. 4k). This ef-
fect is caused by the rotation of the rotor, which transports
higher-momentum air counterclockwise, resulting in a wake
deflection to the left at z = 125 m (Fig. 4c). Consequently,
the opposite situation prevails at z = 75 m (Fig. 4k). As the
inflow veer contribution to wake deflection is much larger
compared to the effect of a clockwise-rotating rotor, the wake
deflection changes from the left in CR_NV (Fig. 4c) to the
right in CR (Fig. 4a) in the upper rotor half and vice versa in
the lower rotor half.
As a next step, the rotational-direction impact in the non-
veered simulations CR_NV and CCR_NV is investigated
(Fig. 4c vs. Fig. 4d, Fig. 4g vs. Fig. 4h, and Fig. 4k
vs. Fig. 4l). The impact of the rotational direction on the
wake is limited to the wake deflection differences at the up-
per (Fig. 4c and d) and the lower (Fig. 4k and l) rotor height,
which are nearly axis-symmetric to y = 0 D and result from
the rotational direction of the rotor. These differences in the
nonveered simulations agree with results of Vermeer et al.
(2003), Shen et al. (2007), Sanderse (2009), Kumar et al.
(2013), Hu et al. (2013), Yuan et al. (2014), Mühle et al.
(2017), and Englberger et al. (2020).
The rotational-direction impact on the wake structure un-
der veering inflow is investigated by a comparison of CCR to
CR (Fig. 4b vs. Fig. 4a, f vs. Fig. 4e, and Fig. 4j vs. Fig. 4i).
In CCR, the wake recovers more rapidly (Fig. 4f vs. Fig. 4e)
and the wake deflection angle is larger (Fig. 4b vs. Fig. 4a and
Fig. 4j vs. Fig. 4i) in comparison to CR. Further, the wake
width is larger in the spanwise direction in CCR in compari-
son to CR (Fig. 4b vs. Fig. 4a, Fig. 4f vs. Fig. 4e, and Fig. 4
vs. Fig. 4i).
The differences in the spanwise wake width and the wake
deflection angle are investigated in more detail with the y–
z cross sections at x = 7 D in Fig. 5 for veering inflow (CR
in Fig. 5a, CCR in Fig. 5b) and no wind veer (CR_NV in
Fig. 5c, CCR_NV in Fig. 5d) with both rotational directions
of the actuator. In the case of no veering inflow, the simulated
wake at x = 7 D retains the shape of the rotor (Fig. 5c). In
the case of a veering inflow, however, the wake in the lower
rotor half is shifted to the left and in the upper rotor half
to the right (Fig. 5a). The striking difference between veer-
ing and nonveering inflow simulations in combination with a
clockwise-rotating actuator corresponds to the inflow profile
(Eqs. 6 and 8), where a veering inflow is characterized by a
wind component from right to left for z < 100 m and from
left to right for z > 100 m, whereas the spanwise inflow ve-
locity is zero in the case of no veer at all rotor heights. The
skewed wake structure under veering inflow resembles those
of the simulations of Abkar and Porté-Agel (2016), Vollmer
et al. (2017), Bromm et al. (2017), Churchfield and Sirnivas
(2018), and Englberger and Dörnbrack (2018a).
Wind Energ. Sci., 5, 1623–1644, 2020 https://doi.org/10.5194/wes-5-1623-2020
A. Englberger et al.: Changing the rotational direction of a wind turbine under veering inflow 1631
Figure 4. Contours of the streamwise velocity u
i,j,k
∗
in meters per
second at z = 125 m in the first two rows, at z = 100 m the third and
fourth row, and at z = 75 m in the last two rows for the simulations
CR, CCR, CR_NV, and CCR_NV, each averaged over 30 min. The
black contours represent the velocity deficit VD
i,j,k
∗
at the same
vertical location.
Further, we compare the differences between a clockwise-
and a counterclockwise-rotating actuator for nonveering and
veering inflow. In the case of no wind veer, the simulated
wake structures of CCR_NV (Fig. 5d) and CR_NV (Fig. 5c)
show no striking difference. In the case of veering inflow,
however, the skewed wake structure differs in CR and CCR
(Fig. 5a and b). Whereas the wake is elliptical in CR, this
shape is stretched in the rotor region in CCR. This difference
in shape explains the difference in the spanwise wake width
at hub height (Fig. 4f) and also in the lower (Fig. 4j) and
the upper (Fig. 4b) rotor part. The wake structure outside the
rotor region also differs between Fig. 5a and b. Due to the
elongation of the elliptical structure in CCR in the rotor re-
gion (Fig. 4b) and approximately the same vertical wake ex-
tension in CCR and CR, the wake deflection angle increases
in the case of CCR (Fig. 5b vs. Fig. 5a), as shown in the lower
rotor half in Fig. 4j vs. Fig. 4i and also in the upper rotor half
in Fig. 4b vs. Fig. 4a.
Figure 5. Contours of the streamwise velocity u
i,j,k
∗
in meters per
second at a downward position of x = 3 D behind the rotor for CR
in (a), CCR in (b), CR_NV in (c), and CCR_NV in (d). The blue
circle represents the circumference of the actuator disc.
A quantitative description of the streamwise velocity dif-
ferences is presented in Fig. 6 at the downwind position
x = 7 D. Figure 6 represents the vertical profiles at y = 0 D
in a and spanwise profiles of u at z = 75 m in b, at z = 100 m
in c, and at z = 125 m in d for both rotational directions
CR and CCR. The heights correspond to Fig. 4. Figure 6e–
h represent the nonveering inflow simulations CR_NV and
CCR_NV. Whereas the vertical and spanwise profiles of CR
and CCR in the case of no inflow veer (_NV) are almost over-
lapping (Fig. 6e–h), there is a difference in the case of veer-
ing inflow (Fig. 6a–d). Firstly, the streamwise wake elonga-
tion difference in Fig. 4f vs. Fig. 4e is represented by larger
u values in the lower and the upper rotor half in the case
of CCR in Fig. 6b and d. The larger wake deflection angle
in CCR in comparison to CR (Fig. 4b vs. Fig. 4a and Fig. 4j
vs. Fig. 4i) is represented by a larger spanwise distance of the
minimum of u from y = 0 D in the case of CCR in the lower
(Fig. 6b) and the upper (Fig. 6d) rotor half. This spanwise
difference in u
min
is accompanied by larger u values in the
case of CCR for y < −1/2 D in the lower rotor part (Fig. 6b)
and for y < 1/2 D in the upper rotor part (Fig. 6d). Secondly,
the difference in the spanwise wake width is represented at
all three heights by a larger 1L
y
with smaller u values in
CCR in the outermost region of the left and the right sectors
in comparison to CR (Fig. 6b–d).
As a final step, the difference in the wake is summarized
by the 30 min time-averaged and rotor-area-averaged stream-
wise velocity u
A
. Figure 7a represents the difference be-
tween clockwise- and counterclockwise-rotating rotors for
https://doi.org/10.5194/wes-5-1623-2020 Wind Energ. Sci., 5, 1623–1644, 2020
1632 A. Englberger et al.: Changing the rotational direction of a wind turbine under veering inflow
Figure 6. Vertical profiles (first column) and horizontal profiles at
z = 75 m (second column), z = 100 m (third column), and z = 125 m
(fourth column) of the 30 min averaged streamwise velocity at
x = 7 D downwind of the actuator for CR and CCR in (a–d),
CR_NV and CCR_NV in (e–h), CR_b and CCR_b in (i–l), CR_u6
and CCR_u6 in (m–p), and CR_u14 and CCR_u14 in (q–t).
a veering inflow and in the case of no wind veer from
x = 4 D to 10 D. At x = 7 D, u
A
is 0.24 m s
−1
larger in the
counterclockwise-rotating rotor simulation CCR in compari-
son to CR, whereas there is no difference between CCR_NV
and CR_NV. According to Fig. 6a–d, these larger u
A
values
in the case of CCR result from larger u values in the upper
and lower sector related to the larger wake deflection angle in
the case of CCR, which compensates for the larger u values
in the outer region of the left and right sectors resulting from
a larger spanwise wake width in the case of CCR.
The previous investigations show a striking dependence of
the rotational direction of the rotor on the wake under veering
inflow, which is qualitatively well explained by the analysis.
A schematic illustration of the deceleration or even reversion
of the spanwise flow if a clockwise-rotating rotor CR inter-
acts with a veering wind is presented in Fig. 8a. The amplifi-
cation of the spanwise flow in the case of a counterclockwise-
rotating rotor CCR interacting with veering inflow is pre-
sented in Fig. 8b.
Figure 7. The rotor- and time-averaged streamwise velocity u
A
presented for a downwind region of [4 D,10 D] with special em-
phasis at x = 7 D for the simulations CR_NV, CCR_NV, CR, CCR,
CR_b, and CCR_b in (a); for different geostrophic wind-values
in (b); for different directional shears in (c); and for different ro-
tational frequencies in (d).
4.2 Veering wind vs. backing wind
According to the analytical results (Fig. 2e vs. Fig. 2h), the
spanwise component v in the wake is expected to be com-
parable for a clockwise-rotating rotor in veering inflow and
a counterclockwise-rotating rotor in backing inflow, as well
as for a clockwise-rotating rotor in backing inflow and a
counterclockwise-rotating rotor in veering inflow. The wake
characteristics resulting from a backing wind with both ro-
tational directions are investigated in the simulations CR_b
and CCR_b and compared to the veering wind cases CR and
CCR in Fig. 9. The parameters applied in the corresponding
simulations are listed in Table 1.
The behavior in the upper and the lower rotor part in Fig. 9
can directly be compared after mirroring at y = 0 D, an effect
resulting from the opposite sign of the directional shear and
1φ in Eqs. (9) and (10). A strong similarity is prevalent in
the streamwise velocity component at hub height (Fig. 9f, g
and e, h), in the lower rotor half (Fig. 9i, l and j, k) as well
Wind Energ. Sci., 5, 1623–1644, 2020 https://doi.org/10.5194/wes-5-1623-2020
A. Englberger et al.: Changing the rotational direction of a wind turbine under veering inflow 1633
Figure 8. Schematic illustration of the rotational direction of the
wake for the following cases: clockwise blade rotation CR with
veering wind in NH (corresponding to backing wind in SH) in (a),
counterclockwise blade rotation CCR with veering wind in NH
in (b), counterclockwise blade rotation with backing wind CCR_b
in NH (corresponding to veering wind in SH) in (c), and clockwise
blade rotation with backing wind CR_b in NH in (d).
as in the upper rotor half (Fig. 9a, d and b, c). The more
rapid wake recovery and the larger spanwise wake width for
CCR and CR_b in comparison to CR and CCR_b are present
at all rotor heights. The larger wake deflection angle in the
upper and the lower rotor half in CCR (Fig. 9b and j) is also
comparable to CR_b (Fig. 9c and k), whereas the smaller
wake deflection angle in CR (Fig. 9a and i) is comparable to
CCR_b (Fig. 9d and l).
The qualitative comparison in Fig. 6i–l shows the differ-
ences from Fig. 9 between CR_b and CCR_b in the case of
streamwise wake elongation, spanwise wake width, and the
wake deflection angle. Further, comparing the backing-wind
situation (Fig. 6i–l) to the veering-wind situation (Fig. 6a–d),
CR_b corresponds to CCR and CCR_b to CR in the verti-
cal profiles (Fig. 6i vs. Fig. 6a) and at hub height (Fig. 6k
vs. Fig. 6c). After mirroring at y = 0 D, CR_b corresponds to
CCR and likewise CCR_b to CR in the lower and the upper
rotor part (compare Fig. 6j to Fig. 6b and Fig. 6l to Fig. 6d).
Expressing the differences between a backing and a veer-
ing wind from both rotational directions of the rotor by
the quantity u
A
in Fig. 7a, the u
A
values are 0.24 m s
−1
larger if a backing wind (CR_b) interacts with a clockwise-
rotating rotor in comparison to a veering wind (CR). Sim-
ilarly, the u
A
values are larger if a backing wind interacts
with a counterclockwise-rotating rotor (CCR_b). Therefore,
1u
A
is the same for CR and CCR_b and likewise for CCR
and CR_b.
The northern hemispheric results of CR and CCR are com-
parable to southern hemispheric CR_b and CCR_b situa-
tions, whereas the northern hemispheric results of CR_b and
CCR_b correspond to CR and CCR in the SH. The schematic
Figure 9. Contours of the streamwise velocity u
i,j,k
∗
in meters per
second at z = 125 m in the first two rows, at z = 100 m the third and
fourth row, and at z = 75 m in the last two rows for the simulations
CR, CCR, CR_b, and CCR_b, each averaged over 30 min. The black
contours represent the velocity deficit VD
i,j,k
∗
at the same vertical
location.
illustration of a backing wind interacting with both rotational
directions is presented in Fig. 8c and d with an amplification
of the spanwise wind component in the case of a backing
wind and a clockwise-rotating rotor CR_b (Fig. 8d) and a
weakening or reversion in the case of a counterclockwise-
rotating rotor CCR_b (Fig. 8c).
4.3 Wind speed
Wind speed may also affect the veering inflow (Eq. 8
via Eq. 6), modifying the spanwise velocity component.
There is no significant impact of u
g
= (6, 10, 14) m s
−1
on the wake elongation, the spanwise wake width,
and the wake deflection angle between clockwise- and
counterclockwise-rotating actuators. Therefore, the contour
plots are not shown. Only a qualitative comparison is pre-
sented in Fig. 6m–p for u
g
= 6 m s
−1
and in Fig. 6q–t for
u
g
= 14 m s
−1
. The occurrence of a wake width as well as
the wake deflection angle difference between clockwise- and
https://doi.org/10.5194/wes-5-1623-2020 Wind Energ. Sci., 5, 1623–1644, 2020
1634 A. Englberger et al.: Changing the rotational direction of a wind turbine under veering inflow
Figure 10. Contours of the streamwise velocity u
i,j,k
∗
in meters
per second for different directional shears at z = 100 m for CR_ds4
in (a), CCR_ds4 in (b), CR in (c), CCR in (d), CR_ds12 in (e),
CCR_ds12 in (f), CR_ds16 in (g), CCR_ds16 in (h), CR_ds20 in (i),
and CCR_ds20 in (j), each averaged over 30 min. The black con-
tours represent the velocity deficit VD
i,j,k
∗
at the same vertical lo-
cation.
counterclockwise-rotating actuators from the reference case
u
g
= 10 m s
−1
(Fig. 6b–d) is independent of u
g
. Only for
smaller velocity values (u
g
= 6 m s
−1
; Fig. 6o) are the hub
height differences less pronounced.
The similarity of the vertical and spanwise profiles for
all geostrophic-wind values in Fig. 6 results in no re-
markable difference in u
A
in Fig. 7b between clockwise-
and counterclockwise-rotating simulations. Independent of
u
g
, the values of u
A
are slightly larger in the case
of counterclockwise-rotating simulations in comparison to
clockwise ones, except the difference in u
A
between
clockwise- and counterclockwise-rotating simulations in-
creases for decreasing u
g
.
4.4 Directional shear
The directional shear is the second contributing parameter
of the veering inflow (Eq. 8), modifying the spanwise ve-
locity component resulting from analysis. The impact of all
five directional-shear values from Table 1 on the wake is in-
vestigated at hub height (Fig. 10) and in the upper (Fig. 11)
and lower (Fig. 12) rotor half. In the clockwise-rotating
as well as the counterclockwise-rotating actuator simula-
tions (Figs. 10–12) the wake recovers more rapidly if direc-
Figure 11. Contours of the streamwise velocity u
i,j,k
∗
in meters
per second for different directional shears at z = 125 m for the same
simulations as in Fig. 10. The black contours represent the velocity
deficit VD
i,j,k
∗
at the same vertical location.
tional shear increases. A larger directional shear represents
a larger turbulence source due to an increase in
∂v
f
∂z
. There-
fore, the simulations with larger directional-shear values re-
sult in higher entrainment rates and a more rapid wake re-
covery. Our simulated dependence of the wake recovery on
the amount of wind veer for clockwise-rotating simulations
is comparable to the numerical results in Fig. 11 of Bhagana-
gar and Debnath (2014).
The magnitude of directional shear affects the wake elon-
gation in dependence on the rotor direction but not to the
same extent in clockwise-rotating simulations in comparison
to counterclockwise-rotating ones. The wake elongation in
CR_ds4 is much longer in comparison to CCR_ds4 (panel a
vs. panel b in Figs. 10–12). It is still larger in CR in com-
parison to CCR (panel c. vs. panel d in Figs. 10–12). A
further increase in the directional shear finally results in a
similar wake recovery of CR_ds12 and CCR_ds12 (panel e
vs. panel f in Figs. 10–12) and a slightly more rapid wake
recovery of CR_ds16 in comparison to CCR_ds16 (panel g
vs. panel h in Figs. 10–12). Comparing the very strong
directional-shear cases CR_ds20 and CCR_ds20 (panel i
vs. panel j in Figs. 10–12), the wake recovery is significantly
faster in CR_ds20. Further, the difference between CR_ds4
and CR is larger in comparison to CCR_ds4 and CCR (pan-
els a, c and panels b, d in Figs. 10–12). This trend continues
for increasing directional shear.
Wind Energ. Sci., 5, 1623–1644, 2020 https://doi.org/10.5194/wes-5-1623-2020
A. Englberger et al.: Changing the rotational direction of a wind turbine under veering inflow 1635
Figure 12. Contours of the streamwise velocity u
i,j,k
∗
in meters
per second for different directional shears at z = 75 m for the same
simulations as in Fig. 10. The black contours represent the velocity
deficit VD
i,j,k
∗
at the same vertical location.
Another difference between clockwise- and
counterclockwise-rotating actuators is the spanwise wake
width (Fig. 10c vs. d). The impact of the directional shear on
the spanwise wake width at hub height results in an increase
in the difference in the spanwise wake width between a
clockwise- and a counterclockwise-rotating simulation
(Fig. 10a, c, e, g, i vs. Fig. 10b, d, f, h, j). In addition, the
wake deflection angle increases for increasing values of the
directional shear. The difference in larger wake deflection
angles in the case of a counterclockwise-rotating actuator in
the upper and the lower rotor part is also prevalent for all
directional-shear values (right column of Figs. 11 and 12,
panels b, d, f, h, j). Further, large values of the directional
shear in combination with a counterclockwise-rotating
actuator leads to a breakup of the wake (panels h and j
in Figs. 11 and 12). This erosion could be related to high
spanwise-velocity values in the case of CCR_ds16 and
CCR_ds20 due to amplification of the inflow and the vortex
spanwise component, which is not the case in CR_ds16 and
CR_ds20 (panels g and i in Figs. 12 and 11).
For a quantitative investigation of the directional-shear im-
pact on the differences in the wake between clockwise- and
counterclockwise-rotating actuators, vertical and horizontal
profiles at x = 7 D for all five cases of different directional-
shear values are presented in Fig. 13. Considering the vertical
profile through y = 0 D (left column of Fig. 13), the vertical
Figure 13. Vertical profiles (first column) and horizontal pro-
files at z = 75 m (second column), z = 100 m (third column), and
z = 125 m (fourth column) of the 30 min averaged streamwise ve-
locity at x = 7 D downwind of the actuator for a directional shear
of 0.04
◦
m
−1
in (a–d), 0.08
◦
m
−1
in (e–h), 0.12
◦
m
−1
in (i–l),
0.16
◦
m
−1
in (m–p), and 0.20
◦
m
−1
in (q–t).
wake extension decreases if the directional shear increases,
as the wake deflection is influenced by the incoming wind
direction at each height (Churchfield and Sirnivas, 2018;
Tomaszewski et al., 2018; Bodini et al., 2017; Englberger and
Lundquist, 2020). This dependency of wake veer on wind
veer is also represented at z = 75 m (Fig. 13b, f, j, n, r) and
at z = 125 m (Fig. 13d, h, l, p, t), where the wake deflection
angle is additionally influenced by the rotational direction of
the actuator. The wake deflection angle is larger if the actu-
ator rotates counterclockwise, independent of the values of
directional shear.
The directional-shear impact on the spanwise wake width
is investigated via the profiles of Fig. 13. Especially at hub
height (Fig. 13c, g, k, o, s), the wake width decreases if the
directional shear increases. This effect can be related to the
increase in skewness in the wake for an increasing direc-
tional shear. Comparing clockwise- and counterclockwise-
rotating actuators, the spanwise wake width is larger in the
case of a counterclockwise-rotating actuator, independent of
the directional-shear value.
https://doi.org/10.5194/wes-5-1623-2020 Wind Energ. Sci., 5, 1623–1644, 2020
1636 A. Englberger et al.: Changing the rotational direction of a wind turbine under veering inflow
Considering the rotor-averaged values u
A
in Fig. 7c, the
rotor-averaged wind speeds are larger for a weak wind
veer in the counterclockwise-rotating actuator simulations
(CCR_ds4) in comparison to the clockwise-rotating ones
(CR_ds4). As the wind veer increases, the difference in u
A
between clockwise- and counterclockwise-rotating disc sim-
ulations decreases. In the case of a moderate to strong wind
veer, u
A
is only slightly larger for the clockwise-rotating ro-
tor CR_ds12. Approaching an even higher directional shear
in the strong and very strong wind shear cases, this differ-
ence between CR_ds16 and CCR_ds16 and likewise between
CR_ds20 and CCR_ds20 increases, whereas now the rotor-
averaged wind speeds are larger for clockwise-rotating actu-
ators in comparison to counterclockwise ones.
Independent of the directional shear, the streamwise-
velocity values at x = 7 D are larger in the case of a
counterclockwise-rotating actuator in the top and the bot-
tom sector (Fig. 13 second and fourth column). The differ-
ence between counterclockwise and clockwise rotation in-
creases in the radial direction away from the nacelle (not
shown). This is related to the larger wake deflection an-
gle in the counterclockwise-rotating case in comparison to
the clockwise case. Also independent of the directional
shear, the streamwise-velocity values are larger in the case
of a clockwise-rotating actuator in the left and right sec-
tors (Fig. 13 third row). This is an effect of the narrower
wake width in the case of a clockwise-rotating actuator.
If the directional shear is small, the larger u values of
counterclockwise-rotating actuators in the top and bottom
sectors are compensating for the larger u values in the case of
a clockwise-rotating actuator in the right and left sectors. If
the rotational direction is very high, the opposite is the case.
4.5 Rotational frequency
The rotational frequency contributes to the wind-turbine
forces in Eq. (1) and modifies the spanwise velocity com-
ponent (Eq. 17). The wake impact of the four rotational-
frequency values from Table 1 is presented at hub height
(Fig. 14), at z = 125 m (Fig. 15), and at z = 75 m (Fig. 16). In
comparison to the impact of a change in the atmospheric pa-
rameters, which was mainly limited to the far wake, the rota-
tional frequency also significantly impacts the near wake. An
increase in the rotational frequency results in a larger mini-
mum value of the velocity deficit (panels g, h vs. panels a, b
in Figs. 15 and 16) and a less rapid wake recovery (panels
g, h vs. panels a, b in Figs. 15 and 16). As the rotational fre-
quency increases, the wake structure differs more between
clockwise- and counterclockwise-rotating actuators. The dif-
ference in the spanwise wake width increases for an increas-
ing rotational frequency at all heights. Further, an increase in
the rotational frequency results in a slightly larger downwind
wake extension in the case of a clockwise-rotating actuator at
all heights. In the case of a counterclockwise-rotating actu-
ator, however, an increase in the rotational frequency results
Figure 14. Contours of the streamwise velocity u
i,j,k
∗
in me-
ters per second for different rotational frequencies at z = 100 m for
CR_l in (a), CCR_l in (b), CR in (c), CCR in (d), CR_h in (e),
CCR_h in (f), CR_vh in (g), and CCR_vh in (h), each aver-
aged over 30 min. The black contours represent the velocity deficit
VD
i,j,k
∗
at the same vertical location.
Figure 15. Contours of the streamwise velocity u
i,j,k
∗
in meters
per second for different rotational frequencies at z = 125 m for the
same simulations as in Fig. 14. The black contours represent the
velocity deficit VD
i,j,k
∗
at the same vertical location.
in a similar downwind wake extension of the velocity deficit
(Eq. 14).
A wake-splitting pattern exists in the upper (Fig. 15f
and h), as well as in the lower (Fig. 16f and h) rotor
part for large rotational-frequency values. The pattern is
similar to the breakup of the wake for large directional-
shear values interacting with a counterclockwise-rotating
actuator in CCR_ds16 and CCR_ds20 (panels h and j in
Wind Energ. Sci., 5, 1623–1644, 2020 https://doi.org/10.5194/wes-5-1623-2020
A. Englberger et al.: Changing the rotational direction of a wind turbine under veering inflow 1637
Figure 16. Contours of the streamwise velocity u
i,j,k
∗
in meters
per second for different rotational frequencies at z = 75 m for the
same simulations as in Fig. 14. The black contours represent the
velocity deficit VD
i,j,k
∗
at the same vertical location.
Figs. 11 and 12). The occurrence of the pattern in combi-
nation with high rotational-frequency values could also be
related to a very large spanwise flow component, now re-
sulting from a large contribution of the vortex. An additional
simulation (not shown) with u
g
= 10 m s
−1
, ds = 0.20
◦
m
−1
,
and = 0.23 s
−1
reinforces the slitting pattern of Figs. 12
and 11h and j, supporting our assumption as to why the
splitting occurs only for counterclockwise-rotating actua-
tors. Further, a similar but less distinctive wake-splitting pat-
tern for a counterclockwise-rotating actuator was observed
in the veer-affected lower rotor half with ds = 0.28
◦
m
−1
and
= 0.12 s
−1
; see Fig. 10f by Englberger et al. (2020).
For a quantitative investigation of the rotational-frequency
impact on the wake differences between clockwise- and
counterclockwise-rotating rotors, the vertical and horizontal
profiles at x = 7 D are presented for all four cases in Fig. 17.
Considering the vertical and spanwise profiles at z = 100 m
(Fig. 17 first and third column), the rotational-direction de-
crease in u results from larger wind-turbine forces due to an
increase in . The difference in the wake defection angle
(Fig. 17 second and fourth column) and in the spanwise wake
width (Fig. 17 second, third, and fourth column) between
clockwise- and counterclockwise-rotating discs increases for
increasing . An increase in further results in two u min-
ima in the lower (Fig. 17j and n) and the upper (Fig. 17l
and p) rotor half and a larger decrease in u approaching
r = R at hub height (Fig. 17k and o) in the counterclockwise-
rotating simulations.
The increase in u in the lower and upper sector com-
pensates for the decrease in the left and right sector for in-
creasing in the case of counterclockwise-rotating discs
(Fig. 17), resulting in larger values of u
A
in Fig. 7d for
Figure 17. Vertical profile (first column) and horizontal profiles at
z = 75 m (second column), z = 100 m (third column), and z = 125 m
(fourth column) of the 30 min averaged streamwise velocity at
x = 7 D downwind of the actuator for a rotational frequency of
= 0.058
◦
s
−1
in (a–d), = 0.12
◦
s
−1
in (e–g), = 0.175
◦
s
−1
in (i–l), and = 0.23
◦
s
−1
in (m–o).
all counterclockwise-rotating simulations. The
u
A
difference
between clockwise- and counterclockwise-rotating actuators
increases for an increasing rotational frequency, which is re-
lated to the splitting of the wake.
5 Comparison to analytic model
The idealized numerical simulations investigated the impact
of the rotational direction of the actuator in combination with
veering inflow, no wind veer, and backing inflow on the wake
of a single wind turbine. The parameter study investigated
the streamwise dependency of the wake on wind speed, di-
rectional shear, and rotational frequency. For a comparison
of the simulated results with the expected results from analy-
sis in Fig. 2, Fig. 18 is plotted for 90
◦
bottom and top sectors
in the range 0 m < r ≤ 50 m (Fig. 1). Figure 2 represents the
results at y = 0 D and z = 75 m as the bottom part of the rotor
disc and at y = 0 D and z = 125 m as the top of the rotor disc.
The general structure (slope, sign-changing point), however,
is independent of the vertical location in the analysis. Only
the magnitude of the spanwise inflow v
f
at x
down
> x
ξ
and of
the spanwise vortex component v
v
at x
down
< x
ξ
are affected
in Fig. 2, as v
f
is height dependent and asymmetric to the
rotor center and v
v
has a radial dependency. Therefore, the
panels of Fig. 18 are directly comparable to those of Fig. 2
https://doi.org/10.5194/wes-5-1623-2020 Wind Energ. Sci., 5, 1623–1644, 2020
1638 A. Englberger et al.: Changing the rotational direction of a wind turbine under veering inflow
Figure 18. Sector averages of v representing the top and
bottom 90
◦
sectors for 0 m < r ≤ 50 m for clockwise- and
counterclockwise-rotating actuators in the corresponding simula-
tion of no veer in (b), a veering wind in (e), and a backing wind
in (h). In the case of a veering wind in (e), moderate parame-
ters of u
g
= 10 m s
−1
, ds = 0.08
◦
m
−1
, and = 0.12
◦
s
−1
are ap-
plied. In the left (a, d, g) and right (c, f, i) column, only one pa-
rameter is changed compared to the veering-wind situation in (e).
Applying low parameters, u
g
= 6 m s
−1
in (a), ds = 0.04
◦
m
−1
in (d), and = 0.058
◦
s
−1
in (g), and applying high parameters,
u
g
= 14 m s
−1
in (c), ds = 0.12
◦
m
−1
in (f), and = 0.175
◦
s
−1
in (i). The plot is directly comparable to Fig. 2 considering the con-
figurations.
regarding the difference in 1u
g
, 1ds, and 1 between low-,
moderate-, and high-value cases.
Comparing the nonveering simulations CR_NV and
CCR_NV (Fig. 18b) to the analysis prediction (Fig. 2b),
v > 0 in the top sector and v < 0 in the bottom sector
both with a clockwise-rotating rotor. In the case of a
counterclockwise-rotating rotor, v in the top sector corre-
sponds to v in the bottom sector of a clockwise-rotating
simulation and vice versa. Only the downwind slope for
x
down
< x
ξ
is much smaller. This results from a different ra-
dial distribution and a smaller absolute value of the wind-
turbine forces applied in the numerical simulations (Eq. 1) in
comparison to the Rankine vortex applied in the theoretical
analysis (Eqs. 15 and 16). Further, the smaller slope in the
numerical simulations can be related to the resolved turbu-
lence and the resulting wake recovery.
Comparing the simulation with moderate-veering inflow
CR and CCR (Fig. 18e) to the analysis predictions (Fig. 2e),
the acceleration in the case of a counterclockwise-rotating
rotor and the weakening in the case of a clockwise-rotating
rotor up to x
down
≈ 10 D are prevalent. The smaller slope val-
ues are for the same reason as in the nonveering case. The
different slope values between the simulations and the anal-
ysis predictions simply result in an upwind shift in the sign-
changing location in the wake. An increase in (Fig. 18i)
approaches the structure predicted by analysis (steeper slope,
flow reversion behind the rotor, downwind shift in the sign-
changing point) of Fig. 2b. The values of applied in the
BEM method to calculate the wind-turbine forces (Eq. 1) are
the same as the values of ω applied in the Rankine vortex
(Eq. 15). Due to the differences in the calculation of the span-
wise flow field between the BEM method and the Rankine
vortex, the near-wake absolute values are not comparable in
Figs. 2 and 18. Considering the backing inflow simulation
(Fig. 18h) and exchanging clockwise and counterclockwise
and likewise top and bottom, it corresponds to the veering
inflow in Fig. 18e, which is predicted by Fig. 2h and e.
The analytic model predicts the same impact of
the geostrophic wind and the directional shear on
the spanwise wake structure (Fig. 2a vs. Fig. 2d
and Fig. 2c vs. Fig. 2f). The general structure at
x
down
< x
ξ
is comparable in the numerical simulations
with u
g
= 6 m s
−1
and ds = 0.08
◦
m
−1
(Fig. 18a) and
u
g
= 10 m s
−1
and ds = 0.04
◦
m
−1
(Fig. 18d) and like-
wise with u
g
= 14 m s
−1
and ds = 0.08
◦
m
−1
(Fig. 18c) and
u
g
= 10 m s
−1
and ds = 0.12
◦
m
−1
(Fig. 18f). Minor differ-
ences exist; e.g., compare the difference between clockwise-
and counterclockwise-rotating simulations at x = 7 D in
Fig. 18a and d. The larger difference between CR_ds4 and
CCR_ds4 in Fig. 18d can be related to a decrease in
∂v
f
∂z
and a smaller amount of resolved turbulence generated by
the inflow with ds = 0.04
◦
m
−1
(Fig. 18d) in comparison to
ds = 0.08
◦
m
−1
(Fig. 18a), whereas the change in u
g
has no
influence on
∂v
f
∂z
. Changing the wind speed and the direc-
tional shear has a significant impact on | v | further down-
wind at x
down
> x
ξ
; e.g., v
20D
in Fig. 18f ≈ 2 · v
20D
in
Fig. 18d. This corresponds to the differences between Fig. 2f
and d at x
down
> x
ξ
.
Changing the rotational frequency of the vortex has its
largest impact on the spanwise wake velocity directly behind
the rotor, whereas an increase in the spanwise vortex com-
ponent v
v
results in a larger amplification of | v | in the case
of a counterclockwise-rotating rotor and a larger weakening
of | v | in the case of a clockwise-rotating rotor (Fig. 18g, e,
and i). This behavior corresponds to the near-wake differ-
ences in Fig. 2g, e, and i. For large enough values of the rota-
tional frequency, the spanwise wake component reverses sign
in the simulation CR_h directly behind the rotor (Fig. 18i).
The comparison of the simulation results with the analysis
predictions can be summarized as follows:
– The simulated amplification or weakening or reversion
of the spanwise inflow wind component in the wake fol-
lows the theoretical analysis in the case of no wind veer,
Wind Energ. Sci., 5, 1623–1644, 2020 https://doi.org/10.5194/wes-5-1623-2020
A. Englberger et al.: Changing the rotational direction of a wind turbine under veering inflow 1639
Figure 19. Sector averages of u representing the top and
bottom 90
◦
sectors for 0 m < r ≤ 50 m for clockwise- and
counterclockwise-rotating actuators for the same simulations as in
Fig. 18.
a veering inflow, and a backing inflow for clockwise-
and counterclockwise-rotating discs. It can be under-
stood and described by the superposition of the rota-
tional flow induced by the disc and the vertical shear of
the incoming wind.
– The agreement of the simulation results with the anal-
ysis predictions proves that the impact of the rotational
direction on the spanwise wake field is determined by
the mean values of the inflow wind field and influenced
by the resulting turbulence.
– The inflow parameters (wind speed and directional
shear) and the rotation rate of the rotor are two counter-
acting processes. The individual magnitudes determine
the differences in the spanwise wake component be-
tween clockwise- and counterclockwise-rotating actua-
tors. The difference increases (decreases) for increasing
(decreasing) values of u
g
, ds, and .
The rotational-direction impact on the spanwise velocity
component in the wake also modifies the streamwise flow
component. The streamwise velocity components in the
wake are shown in Fig. 19 for the same sectors and sim-
ulations as in Fig. 18. The larger values in the top sector
in comparison to the bottom sector result from the height-
dependent streamwise velocity (Eq. 6) with larger values in
the upper rotor half. In the case of no wind direction change
with height (_NV, Fig. 19b), the u values are independent of
the rotational direction of the actuator. In the case of a veer-
ing (backing) inflow (Fig. 19e and b), the streamwise wake
velocity is larger in the case of CCR (CR_b) in comparison to
CR (CCR_b) in both sectors. The parameters under veering
inflow impact the difference 1u between counterclockwise-
and clockwise-rotating actuators in the corresponding sector
(Fig. 19a, d, g and c, f, i). An increase in u
g
, ds, or results
in larger 1u values (Fig. 19c, f, i), whereas smaller parame-
ter values decrease 1u (Fig. 19a, d, g). The difference 1u in
the left and right sectors is much less distinct in comparison
to the top and bottom sectors (not shown).
The rotational-direction impact on the wake can be sum-
marized as follows:
– A rotational-direction impact on the streamwise veloc-
ity components in the wake exists only in the case of a
veering (or backing) inflow.
– In the case of veering inflow in the NH the spanwise
wake width (1L
y
) as well as the wake deflection angle
(1) is larger in the case of a counterclockwise-rotating
actuator CCR (Fig. 20). This behavior is independent of
the magnitude of the parameters.
– Increasing the magnitudes of the directional shear
ds or the rotation rate increases the spanwise
wake width difference (1L
y
) and the wake deflec-
tion angle difference (1) between a counterclockwise-
and a clockwise-rotating actuator. The impact of the
geostrophic wind u
g
is much less pronounced.
– An increase in u
g
or likewise a decrease in re-
sults in a more rapid wake recovery. Increasing ds,
there is no wake difference between a clockwise- and a
counterclockwise-rotating actuator for a specific direc-
tional shear ds
c
. If ds < ds
c
, the streamwise velocity is
larger in the case of a counterclockwise-rotating rotor,
whereas for ds > ds
c
, the streamwise velocity is larger
in the case of a clockwise-rotating rotor. Approaching
smaller or larger values of the directional shear, 1u in-
creases between a clockwise- and a counterclockwise-
rotating actuator.
6 Conclusions
We investigate the impact of the rotational direction on the
wake of a wind turbine for veering and backing inflow con-
ditions, as well as in the case of no wind veer in both hemi-
spheres, using idealized LESs in comparison to a simple
analytic model. In addition, the impact of the geostrophic
wind and the directional shear as well as the impact of
the rotational frequency on the wake differences between
clockwise- and counterclockwise-rotating wind turbines was
investigated in the case of veering inflow.
https://doi.org/10.5194/wes-5-1623-2020 Wind Energ. Sci., 5, 1623–1644, 2020
1640 A. Englberger et al.: Changing the rotational direction of a wind turbine under veering inflow
Figure 20. Schematic illustration of the difference in the spanwise wake width (L
y
) and the wake deflection angle () between clockwise-
rotating CR and counterclockwise-rotating CCR actuators. The parameter impact on these wake differences is represented by 1L
y
and 1.
The differences in 1L
y
are valid over the whole rotor, whereas = 1 = 0 at hub height as v
f
(z
h
) = 0 (Eq. 8).
The rotational direction of a wind turbine has only a minor
impact on the wake in the case of no wind veer. This result
from the numerical experiments is consistent with previous
investigations by Vermeer et al. (2003), Shen et al. (2007),
Sanderse (2009), Kumar et al. (2013), Hu et al. (2013), Yuan
et al. (2014), Mühle et al. (2017), and Englberger et al.
(2020). An inflow without wind veer is a typical daytime sit-
uation and also occurs in the evening transition of the diurnal
boundary layer evolution, when the flow is still influenced by
daytime turbulence.
In the case of veering or backing inflow, however, the wake
characteristics (streamwise wake elongation, spanwise wake
width, wake deflection angle) depend significantly on the ro-
tational direction. Veering and backing inflow are character-
istic nighttime situations of the boundary layer flow if no
other processes such as topographically induced circulations
or large-scale weather systems prevent the establishment of
an SBL regime. Veer within the wind-turbine rotor layer has
been observed with several field campaigns with towers and
lidars (Walter et al., 2009; Sanchez Gomez and Lundquist,
2020; Bodini et al., 2019, 2020), and veer throughout the
boundary layer has been observed globally using radiosonde
datasets (Lindvall and Svensson, 2019).
Under veering inflow in the NH (backing inflow in the
SH), the spanwise wake width and the wake deflection an-
gle are larger for a counterclockwise-rotating (clockwise-
rotating) actuator in comparison to a clockwise-rotating one.
An increase (decrease) in the directional shear in the at-
mospheric flow or in the rotational frequency of the ro-
tor increases (decreases) the differences in the spanwise
wake width and the wake deflection angle. The wind speed
does not impact these wake characteristics significantly.
In locations with veering inflow in the NH (backing in-
flow in the SH) and directional-shear values ds < ds
c
with
0.12
◦
m
−1
< ds
c
< 0.16
◦
m
−1
, the streamwise velocity is
larger in the case of a counterclockwise-rotating (clockwise-
rotating) rotor. These differences apply to the wake rang-
ing from x = 4 D to at least x = 10 D downwind. For less
common higher values of the directional shear ds > ds
c
, the
streamwise velocity is larger in the case of a clockwise-
rotating (counterclockwise-rotating) rotor in the NH (SH).
Different operating conditions (e.g., yaw control) of up-
wind turbines are already applied to mitigate downwind im-
pacts in wind parks (Fleming et al., 2019). This work sug-
gests that counterclockwise-rotating blades in the case of
veering inflow and clockwise-rotating blades in the case of
backing inflow in the NH (and vice versa in the SH) could
have benefits as well. The wake deflection angle becomes
larger if the spanwise flow component is amplified by the
vortex induced by the rotating wind turbine. This process oc-
curs independent of the magnitude of the parameter values
applied in the numerical simulations.
As the numerical results of this study arise from an ide-
alized parameter study employing specific assumptions, they
have limitations. For example, the turbulent perturbations ap-
plied in the numerical simulations are incorporated via a sim-
ple turbulence parametrization. The imposed turbulence pa-
rameters were retrieved from a precursor LES and no real-
time wind and potential-temperature profiles are applied.
Particularly, the impact of the rotational direction on a wind-
turbine wake under veering (or backing) inflow resulted from
basic analytical predictions and was compared with the nu-
merical model. However, the impact of rotational directions
has never been measured, as no counterclockwise-rotating
wind turbines currently exist. Despite the limitations of this
numerical study, the simple analysis as well as the idealized
parameter study shows a consistent and clear impact of the
rotational direction of a wind turbine on the wake flow dur-
ing conditions for which the wind direction turns with height.
To explore a more comprehensive assessment of the wake
impact, further investigations would be interesting: the in-
vestigation of the nonlinearity of the interaction process, nu-
merical simulations applying the turbulence of an SBL pre-
cursor simulation for different strengths of stratification and
directional shears, or even considering a low-level jet at the
rotor height. Topography could influence the wake dynamic
explored here. We have assessed the wake of an individual
turbine, but these results could be extended to a large farm
Wind Energ. Sci., 5, 1623–1644, 2020 https://doi.org/10.5194/wes-5-1623-2020
A. Englberger et al.: Changing the rotational direction of a wind turbine under veering inflow 1641
in which the presence of upwind turbines could affect turbu-
lence intensity, which probably affects the magnitude. How-
ever, an important point will be to prove the theoretically pre-
dicted effect resulting from superposition of inflow veer with
the vortex component on the wake with measurements.
Finally, the overall assessment of the impact of these re-
sults depends on the frequency of occurrence of veering in-
flow. Only limited sets of long-term observations provide
an assessment of the frequency of veering (Walter et al.,
2009; Sanchez Gomez and Lundquist, 2020; Bodini et al.,
2019, 2020) in the wind-turbine rotor layer. The global cli-
matology of veer throughout the atmospheric boundary layer
based on radiosonde data (Lindvall and Svensson, 2019) sug-
gests that veer occurs broadly in midlatitudes and polar re-
gions, but further investigation is required to assess if that
boundary layer veer broadly affects wind energy generation.
https://doi.org/10.5194/wes-5-1623-2020 Wind Energ. Sci., 5, 1623–1644, 2020
1642 A. Englberger et al.: Changing the rotational direction of a wind turbine under veering inflow
Appendix A: Turbulence parametrization
The turbulence parametrization of Englberger and Dörnbrack
(2018a) is applied in the simulations of this work. The main
part is conducted with α = 0.3, α
u
= 0.15, α
v
= 0.24, and
α
w
= 0.13. These values are nighttime representations fol-
lowing Table 1 of Englberger and Dörnbrack (2018b). Fig-
ure A1 presents the reference CR and CCR wind-turbine
simulation applied in this work at z = 125 m in a and b,
at z = 100 m in e and f, and at z = 125 m at i and j. Fur-
ther, simulation results α = 0.3 and α
i
∗
,j,k
= 0 are presented
at z = 125 m in c and d, at z = 100 m in g and h, and at
z = 125 m in k and l. Panels a and b are the reference simula-
tions CR and CCR with veering inflow. Panels c and d corre-
spond to α = 0.3, panels e and f to α = 0.5, and panels g and h
to α = 0.7, with α
i
∗
,j,k
= 0 in all three cases. The streamwise
velocity at hub height, as well as in the lower and the upper
rotor half, shows similar characteristics of the near-wake ve-
locity deficit maximum, the streamwise wake elongation, the
spanwise wake width, and the wake deflection angle. Only
the strength of occurrence of these wake characteristics de-
pends on the turbulent intensity, which is larger in the case of
α
i
∗
,j,k
= 0. This reinforces the assumption that wake charac-
teristic differences depend on the mean wind profile, which
is the same in all simulations of Fig. A1 and is not an effect
of the applied turbulence parametrization.
Figure A1. Contours of the streamwise velocity u
i,j,k
∗
in meters
per second at z = 125 m in the first two rows, at z = 100 m the third
and fourth row, and at z = 75 m in the last two rows for the simula-
tions CR, CCR, CR_α, and CCR_α, each averaged over 30 min. The
black contours represent the velocity deficit VD
i,j,k
∗
at the same
vertical location.
Wind Energ. Sci., 5, 1623–1644, 2020 https://doi.org/10.5194/wes-5-1623-2020
A. Englberger et al.: Changing the rotational direction of a wind turbine under veering inflow 1643
Data availability. Currently, the data are not publicly available.
Author contributions. All authors conceived the idea. AE per-
formed the simulations and prepared the manuscript with contribu-
tions from both co-authors.
Competing interests. The authors declare that they have no con-
flict of interest.
Acknowledgements. The authors gratefully acknowledge the
Gauss Center for Supercomputing e. V. (http://www.gauss-centre.
eu, last access: 19 November 2020) for funding this project by pro-
viding computing time on the GCS supercomputer SuperMUC at
the Leibniz Supercomputing Center (LRZ; http://www.lrz.de, last
access: 19 November 2020).
Financial support. The article processing charges for this open-
access publication were covered by a Research Center of the
Helmholtz Association.
Review statement. This paper was edited by Sandrine Aubrun
and reviewed by Paul van der Laan and two anonymous referees.
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