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**Research articles**
16 Nov 2018

**Research articles** | 16 Nov 2018

Blind test comparison on the wake behind a yawed wind turbine

^{1}Faculty of Environmental Sciences and Natural Resource Management, Norwegian University of Life Sciences, Ås, Norway^{2}ForWind – Center for Wind Energy, Institute of Physics, University of Oldenburg, Oldenburg, Germany^{3}Department of Energy and Process Engineering, Norwegian University of Science and Technology, Trondheim, Norway^{4}Siemens PLM Software, London, UK^{5}Department of Mechanical Engineering, Politecnico di Milano, Milan, Italy^{6}Facultad de Ingeniería, Universidad de la República, Montevideo, Uruguay^{7}Linné FLOW Centre and Swedish e-Science Research Centre (SeRC), Department of Mechanics, KTH Royal Institute of Technology, Stockholm, Sweden^{8}Fraunhofer IWES, Oldenburg, Germany

Abstract

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This article summarizes the results of the “Blind test 5”
workshop, which was held in
Visby, Sweden, in May 2017. This study compares the numerical predictions of
the wake flow behind a model wind turbine operated in yaw to experimental
wind tunnel results. Prior to the workshop, research groups were invited to
predict the turbine performance and wake flow properties using computational
fluid dynamics (CFD) methods. For this purpose, the power, thrust, and yaw
moments for a 30^{∘} yawed model turbine, as well as the wake's mean and
turbulent streamwise and vertical flow components, were measured in the wind
tunnel at the Norwegian University of Science and Technology (NTNU). In order
to increase the complexity, a non-yawed downstream turbine was added in a
second test case, while a third test case challenged the modelers with a new
rotor and turbine geometry.

Four participants submitted predictions using different flow solvers, three of which were based on large eddy simulations (LES) while another one used an improved delayed detached eddy simulation (IDDES) model. The performance of a single yawed turbine was fairly well predicted by all simulations, both in the first and third test cases. The scatter in the downstream turbine performance predictions in the second test case, however, was found to be significantly larger. The complex asymmetric shape of the mean streamwise and vertical velocities was generally well predicted by all the simulations for all test cases. The largest improvement with respect to previous blind tests is the good prediction of the levels of TKE in the wake, even for the complex case of yaw misalignment. These very promising results confirm the mature development stage of LES/DES simulations for wind turbine wake modeling, while competitive advantages might be obtained by faster computational methods.

How to cite

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How to cite.

Mühle, F., Schottler, J., Bartl, J., Futrzynski, R., Evans, S., Bernini, L., Schito, P., Draper, M., Guggeri, A., Kleusberg, E., Henningson, D. S., Hölling, M., Peinke, J., Adaramola, M. S., and Sætran, L.: Blind test comparison on the wake behind a yawed wind turbine, Wind Energ. Sci., 3, 883-903, https://doi.org/10.5194/wes-3-883-2018, 2018.

1 Introduction

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Wind turbine wake interaction has become a major topic in wind
energy research during the last decades. The power drop between the first and
second turbine can be up to 35 % in an offshore installation, when the
turbines are aligned with the wind direction, while the averaged losses due
to wake interactions are estimated to range between 10 % and 20 %
(Barthelmie et al., 2009). Furthermore, wind turbine wakes show increased levels
of turbulent kinetic energy (TKE), which potentially affects fatigue loads of
downstream turbines. Consequently, the prediction of the wake's mean and
turbulent characteristics is highly important in the wind farm planning
process in order to optimize farm layout and control. For this purpose, the
development of simple analytical wake models started already 40 years ago and
is still ongoing. However, these models only give predictions of the mean
velocity deficit (Polster et al., 2018). For a more accurate simulation of the
wake flow, advanced computational fluid dynamics (CFD) tools based on
Navier–Stokes solvers are used. It is necessary to validate these numerical
tools against experimental data sets to determine their accuracy. Therefore,
a series of blind tests providing detailed flow measurement data was
initiated at NTNU in 2011. In Blind test 1 the performance of a
single turbine as well as the mean streamwise velocity and TKE in the wake
for distances up to 5*D* behind the turbine was compared, *D* being the rotor
diameter. Eight different research groups participated in the workshop,
contributing various types of simulations ranging from Reynolds-averaged
Navier–Stokes (RANS) simulations to LESs. The performance predictions showed
a considerable spread around the experimental results while the prediction of
wake turbulence was scattered by several orders of magnitude, as summarized
by Krogstad and Eriksen (2013). For the next blind test the complexity was increased
by adding a second turbine operating in the wake of the first turbine.
Modelers were asked to simulate the performance of both turbines and the wake
formed behind the downstream turbine. For this blind test, nine predictions
were submitted by eight organizations. The results reported by
Pierella et al. (2014) still showed a large spread in performance and also the
predictions of the wake properties varied significantly. To further
investigate the difference between experimental results and numerical
simulations a third blind test was realized, in which the complexity was
again increased by applying a lateral offset of half a rotor diameter to the
same turbine array. While the performance was predicted fairly well, the
simulations of the asymmetric wake showed large uncertainties in predicting
turbulence (Krogstad et al., 2015). The focus of the fourth blind test was the
influence of different inflow conditions. Therefore, the wake behind a single
turbine was investigated at three different downstream distances for a
low-turbulent, a high-turbulent, and a turbulent shear inflow. Furthermore
the modelers were asked to predict the performance of an aligned turbine
array. This blind test attracted five groups, who all managed to predict the
performance of the upstream turbine fairly well. Nevertheless, the scatter in
the downstream turbine's performance was still significant. The mean wake
properties were generally predicted well, while the turbulence predictions
still showed a large spread, as shown by Bartl and Sætran (2017).

During the last years CFD models were constantly improved, both by increasing
their accuracy and by reducing computational costs. In order to give the
model developers the possibility to test their CFD models in a complex wake
flow, a fifth blind test was initiated, challenging the modelers with the
dynamic flow situation of a yawed wind turbine. The wakes behind two
different turbines and two inline turbines were investigated. Yaw
misalignment is currently a widely discussed topic in wind energy research.
Intentional yaw misalignment of an upstream turbine in a wind farm is deemed
to have a large potential for increasing the farm's efficiency
(Fleming et al., 2014). A first comparison of CFD results to experimental data
on yawed wind turbines was part of the so-called Mexnext project
(Schepers et al., 2014), in which blade loads and wake data were measured on a
model wind turbine of *D*=4.5 m operated in yaw. Even though the analysis
investigated numerical flow predictions of a yawed rotor, there is need for a
deeper investigation of wake properties behind yawed wind turbines. By
increasing the complexity with respect to previous blind tests, the wake
behind a yawed wind turbine is considered to be a challenging task for
simulations.

The work is organized as follows. Section 2 introduces the experimental setup including a presentation of the model wind turbines and the wind tunnel and inflow conditions as well as a description of the investigated test cases. Section 3 explains the methods used in the study, including descriptions of the measurement technique, the measurement uncertainty, the applied CFD codes, and the methods used for comparison. In Sect. 4 the experimental results and the numerical predictions for power, thrust, yaw moments, and wake characteristics are presented and compared. Section 5 discusses the findings of the study before the conclusions are stated.

2 Experimental setup

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In this blind test experiment three different turbine geometries were used.
For the purpose of yaw experiments, a new turbine test rig was constructed at
NTNU, which is called the Laterally Angled Rotating System 1 (LARS1). It
features a shorter nacelle and slimmer tower compared to the turbines used in
previous blind tests in order to minimize the effects on the wake, as shown
in Fig. 1a. A detailed description and technical drawings of
all turbines are presented in the invitation document to the blind test
(Sætran et al., 2018). The 3-bladed rotor is milled from aluminum and is based on
the NREL S826 airfoil. It has a diameter of *D*_{LARS1}=0.984 m and
is identical to the rotor used in previous blind tests, a detailed
description of the rotor can be found in Krogstad and Lund (2012). At its design
tip speed ratio *λ*=6 and *u*_{ref}=10.0 m s^{−1}, the
turbine experiences a chord-based Reynolds number at the blade tips of around
*Re*${}_{\mathrm{tip},\phantom{\rule{0.125em}{0ex}}\mathrm{NTNU}}=\mathrm{1.1}\times {\mathrm{10}}^{\mathrm{5}}$.

NTNU's model wind turbine called T2 was already used in previous blind test experiments. The sketch in Fig. 1b shows that T2 has exactly the same rotor as LARS1, while the nacelle and tower structures are significantly bigger and of a different shape. The turbine is used as a non-yawed downstream turbine in the investigation of an aligned turbine array.

The third turbine used in this blind test is the model wind turbine designed
by ForWind at the University of Oldenburg. For the experiments in the NTNU
wind tunnel, the turbine's hub height was increased with four cylindrical
rods, in order to be operated at a height, comparable to the NTNU turbines.
The turbine has a smaller rotor diameter of *D*_{ForWind}=0.580 m
and is sketched in Fig. 1c. The rotor is based on the SD7003
airfoil and is manufactured using a synthetic compound. A detailed
description can be found in Schottler et al. (2016). It has the same design
tip speed ratio *λ*=6 as the NTNU turbines. For safety reasons, it
was operated at a lower inflow velocity of *u*_{ref}=7.5 m s^{−1}, which results in a chord-based Reynolds number at the tips
of around *Re*${}_{\mathrm{tip},\phantom{\rule{0.125em}{0ex}}\mathrm{ForWind}}=\mathrm{6.4}\times {\mathrm{10}}^{\mathrm{4}}$.

The NTNU and ForWind rotors are based on two different airfoils. The NREL
S826 airfoil, which is used from root to tip for the NTNU rotor, was
originally designed for application in the tip region of full-scale wind
turbines, a detailed description can be found in Somers (2005). It is
designed for Reynolds numbers of *Re*$\phantom{\rule{0.125em}{0ex}}\approx \mathrm{1.0}\times {\mathrm{10}}^{\mathrm{6}}$,
which is around 1 order of magnitude higher as the Reynolds number at the
rotor tip in the presented experiments. Nevertheless, experimental data sets
for airfoil performance at the lower Reynolds range around
*Re*$\phantom{\rule{0.125em}{0ex}}\approx \mathrm{1.0}\times {\mathrm{10}}^{\mathrm{5}}$ were measured at Denmark's Technical
University (DTU; Sarlak et al., 2018) and NTNU (Bartl et al., 2018c). In
Fig. 2 the airfoil polars from the DTU experiments at
*Re*$\phantom{\rule{0.125em}{0ex}}=\mathrm{1.0}\times {\mathrm{10}}^{\mathrm{5}}$ are compared to a standard set of lift and
drag coefficients calculated for *Re*$\phantom{\rule{0.125em}{0ex}}=\mathrm{1.0}\times {\mathrm{10}}^{\mathrm{5}}$ in XFoil,
which was provided in the invitation document (Sætran et al., 2018). It can be seen
that the drag coefficient *C*_{D} is very different and the lift
coefficient *C*_{L} is significantly diverging from an angle of
attack, *α*, of approximately 4^{∘} between the experimental and
XFoil data. This difference is very distinct for high angles of attack that
may occur close to stall.

The ForWind rotor is based on the SD7003 airfoil that is defined in detail in
Selig et al. (1995). It is specifically designed for low Reynolds numbers and
is thus well suited for wind tunnel experiments. In Selig et al. (1995) two
experimental data sets for *Re*$\phantom{\rule{0.125em}{0ex}}=\mathrm{6.4}\times {\mathrm{10}}^{\mathrm{4}}$ and
*Re*$\phantom{\rule{0.125em}{0ex}}=\mathrm{1.02}\times {\mathrm{10}}^{\mathrm{5}}$ are presented. They are in good agreement
with XFoil data sets for *Re*$\phantom{\rule{0.125em}{0ex}}=\mathrm{5.0}\times {\mathrm{10}}^{\mathrm{4}}$ and *Re*$\phantom{\rule{0.125em}{0ex}}=\mathrm{1.0}\times {\mathrm{10}}^{\mathrm{5}}$ that were provided to the participants.

All the experimental data were measured in the closed-loop wind tunnel at the Department of Energy and Process Engineering at NTNU in Trondheim. The wind tunnel has a test section length of 11.5 m, a width of 2.7 m, and a height of 1.8 m. The reference coordinate system is pictured in Fig. 3 and a detailed description can be found in Sætran et al. (2018).

For all test cases a nonuniform shear flow was generated by a grid at the inlet of the test section. The grid is built from wooden bars with a cross section of 0.047 m×0.047 m. In the horizontal direction the bars are evenly distributed with a distance of 0.24 m between the edges of the bars. In the vertical direction the mesh size increases with increasing height from a clearance of 0.016 m close to the floor to an opening of 0.30 m underneath the roof. The grid has a total solidity of about 34 % in the wind tunnel cross section. The shear profile can be described by the power law

$$\begin{array}{}\text{(1)}& {\displaystyle \frac{\stackrel{\mathrm{\u203e}}{u}}{{u}_{\mathrm{ref}}}}={\left({\displaystyle \frac{y}{{y}_{\mathrm{ref}}}}\right)}^{\mathit{\alpha}}.\end{array}$$

The power law describes the wind speed $\stackrel{\mathrm{\u203e}}{u}$ as a function of the
height *y* provided that the reference wind speed *u*_{ref} is known
at a reference height *y*_{ref}. The strength of the shear is
described by the power law coefficient *α*. The shear grid used in the
experiments was designed to obtain an exponent of *α*=0.11.

As the velocities of the shear profile vary in height and are nonuniform over
the rotor area, the reference wind speed *u*_{ref} is defined at the
turbine hub height as shown in Fig. 4a. Furthermore, the
velocity profile approximated by Eq. (1) matches well with
the measured velocities, having a maximum deviation of ±1.0 %.
Figure 4b shows the normalized vertical velocity component of
the inflow for the NTNU turbine. It can be seen that the vertical flow
component *v* is negative, which creates a slight downflow in the wind
tunnel. The deviations in *v* from zero were not known at the time the blind
test invitation was sent out, in which a zero velocity component for *v* was
assumed. In order to take this into account, in the comparison, *v* at the
inlet is subtracted from the vertical velocity component that is measured in
the wake at the same *y* position.

The turbulence intensity (TI) of the inflow is shown in
Fig. 4c. As expected, the turbulence decays with increasing
downstream distance. At the position of the NTNU turbine the turbulence
intensity is measured to be TI =10.0 % at hub height. The integral
length scales *L*_{uu} are calculated from hot-wire measurements of the
streamwise velocity fluctuation *u*^{′} and the dissipation rate of the TKE *E*,
by applying $E=\mathrm{3}/\mathrm{2}A\frac{u{{}^{\prime}}^{\mathrm{3}}}{{L}_{uu}}$, where *A*≈1,
taken from Krogstad and Davidson (2010). This results in *L*_{uu}=0.097 m at the
position of the NTNU turbine. The ForWind turbine was placed 5*D* (*D*=*D*_{LARS1}) behind the shear grid and thus experienced a lower
turbulence intensity of TI =5.2 %. The integral length scale,
however, increased to *L*_{uu}=0.167 m at this position. The third
investigated streamwise position is 6*D* behind the NTNU turbine. At this
position the turbulence has further decayed to TI =4.1 %. The
corresponding integral length scale at this position is *L*_{uu}=0.271 m.

In this blind test experiment the modelers were asked to simulate three test
cases. In test case 1 the flow 3*D* and 6*D* behind the yawed turbine LARS1
and its performance, thrust force, and yaw moment are investigated. The grid
at the inlet is located −2*D* upstream of the turbine location at $x=-\mathrm{2}D$.
The inflow velocity is adjusted to *u*_{ref}=10.0 m s^{−1} and
the turbulence intensity is TI =10.0 % at the turbine's position.
The turbine's hub height is in the center of the wind tunnel at
*h*_{hub}=0.89 m. LARS1 is yawed to ${\mathit{\gamma}}_{\mathrm{LARS}\mathrm{1}}=+\mathrm{30}{}^{\circ}$ and operated at its design tip speed ratio of
*λ*_{LARS1}=6 throughout all measurements. In test case 2 a
turbine operating in the wake of a yawed upstream turbine is investigated.
Therefore, the setup of test case 1 is extended with the turbine T2 located
*D* behind the upstream turbine LARS1. In contrast to LARS1, T2 is not yawed
(*γ*_{T2}=0^{∘}). As the downstream turbine is impinged by
a partial wake of the upstream turbine, its optimum tip speed ratio is
reduced to *λ*_{T2}=5, taking into account that the tip speed
ratio is based on the constant reference velocity *u*_{ref}=10.0 m s^{−1} upstream of the two-turbine array. This test case
investigates to what degree a partial wake impact can deflect the wake behind
a non-yawed downstream turbine. This has recently been investigated in a LES
study by Fleming et al. (2018). In test case 3, similar to test case 1, the
flow 3*D* and 6*D* (*D*=*D*_{ForWind}) behind the ForWind turbine is
investigated. The turbine is located at *x*=3*D* (*D*=*D*_{LARS1}),
which resulted in a lower turbulence intensity of TI =5.2 % at the
turbine position. The hub height is set to *h*_{hub}=0.89 m and the
inflow velocity is reduced to *u*_{ref}=7.5 m s^{−1}.
Corresponding to test case 1 the turbine is yawed for
*γ*_{ForWind}=30^{∘} and is operated at its optimum tip
speed ratio of *λ*_{ForWind}=6. All setup parameters for test
cases 1–3 are summarized in Table 1 and a detailed
description can be found in Sætran et al. (2018).

3 Methods

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The *u*- and *v*-velocity components in the wake were measured using a
two-component FiberFlow laser Doppler velocimetry (LDV) system from Dantec
Dynamics. The LDV probe was placed inside the wind tunnel on a traverse
system. For each measurement point, 5.0×10^{4} samples were recorded.
The sampling frequency was adjusted by controlling the particles in the flow,
ranging from 1500 to 2000 Hz, which resulted in an average sampling time of
approximately 25–33 s.

The thrust force and yaw moments acting on the upstream and downstream turbine were measured separately using a Schencker six-component force balance, which was installed under the wind tunnel floor. The balance also served as a turning table allowing an exact adjustment of the yaw angle. For the rotor thrust only the load cell parallel to the flow was taken into account. The yaw moment was calculated from a moment equilibrium of three measured forces in the horizontal plane (referenced to the rotor center).

The aerodynamic power *P* of the NTNU rotors was measured using the test rig
of turbine T2. This turbine is equipped with an optical RPM sensor
(revolutions per minute) and a
torque transducer in the hub. Thus, the torque *T* and the rotational speed
*ω* of the turbine could be simultaneously measured so that $P=\mathit{\omega}\cdot T$.

The experimentally measured values feature several uncertainties. The
statistical uncertainties in every sample of the mean velocity, power,
thrust, and yaw moments are calculated based on a 95 % confidence level
according to the procedure described in Wheeler and Ganji (2010). The
uncertainty for the power measurements is calculated to be within ±3 %, while the force measurement uncertainty is slightly lower (±2 %). The exact values for all measured points are presented as error
bars in the plots for the power coefficients *C*_{P}, the thrust
coefficients *C*_{T}, and the yaw moments ${M}_{y}^{*}$. The uncertainties
for the mean streamwise velocities *u* in the wake are calculated to be
smaller than ±1 %. The uncertainties for the vertical velocity
component *v* are slightly higher due to the correction by the inlet
component. In order to determine the inaccuracy in the TKE measurements, the
method proposed by Benedict and Gould (1996) was applied. The uncertainties for a
95 % confidence level are found to be below ±2 % in the wake. It
should be noted that the coarse measurement grid slightly influences the
position of the TKE peaks.

Siemens PLM Software from the United Kingdom (Siemens), the Department of Mechanical Engineering of the Politecnico di Milano in Italy (POLIMI), the Facultad de Ingeniería of the Universidad de la República in Uruguay (UdelaR), and KTH Mechanics Department from the Royal Institute of Technology in Sweden (KTH) participated in the blind test and submitted computational results. For clarity, only the abbreviations will be used in the following. A summary of the simulation methods and mesh properties is presented in Table 2.

Siemens, who previously participated in blind test experiments as CD-adapco,
used the finite volume code STAR-CCM+ v12.04 to mesh and solve all three test
cases. Each simulation resolved the rotor, nacelle, and tower structure
completely, and used the hybrid method improved delayed detached eddy
simulation (IDDES), which resolves the energy-carrying eddies in the free
stream and solves the boundary layer flow with RANS. The Spalart–Allmaras
model was used for closure of the turbulence equations, and the fluid was
considered incompressible. Convective fluxes used a MUSCL third-order scheme
(monotonic upwind scheme for conservation laws), while time was discretized using a second-order implicit
scheme. Each set of blades and hub was contained inside a cylindrical,
rotating volume which was meshed with polyhedral cells, whereas the main
domain used trimmed cells, resulting in a hexahedral dominant mesh in which a
small proportion of cells was trimmed near the boundaries. Due to the
rotation of the cylindrical volumes, the mesh was not conformal at the
interface between the two regions, and flow quantities were interpolated from
one volume to another. All wall surfaces, including the wind turbine bodies
and the wind tunnel walls, were covered in several layers of prismatic cells
to improve the resolution of boundary layers. The resulting *y*^{+} values
were below 1 on the turbine bodies, and around 30 on the wind tunnel walls.
The smallest cell size on the surface of the turbine bodies was 0.3 mm,
typically found at the leading edge of the blades. The characteristic cell
size in the rotating regions was 10 mm, which was also the cell size used in
the wake of the rotors. The rest of the domain had a characteristic cell size
of 20 mm. This resulted in meshes of 29×10^{6}, 35×10^{6},
and 17×10^{6} cells for cases 1, 2, and 3 respectively.

While a rigorous mesh dependency study was not performed, the mesh sizes were
based on previous experience and expected to perform well with an affordable
amount of cells. All simulations were run with a time step of $\mathrm{1.0}\times {\mathrm{10}}^{-\mathrm{4}}$ s, which was chosen to strike a balance between accuracy and
computational cost. This value satisfies a number of criteria related to the
rotation of the rotor regions; namely, that the rotors turn by less than
1^{∘} per time step, and that the mesh is moved
by only half the cell size at the interfaces between rotating regions and the
rest of the domain. Furthermore, it was verified a posteriori that the
convective Courant number virtually never exceeded 0.3 in the wake of the
turbines. Admittedly, given the small cell size used to mesh the blades, the
time step causes the blades to move by several cell sizes each time step, and
the Courant number to well exceed 1, particularly so near the blade tips.
While this limits the ability to accurately resolve the flow at the blades,
it was deemed sufficient to produce accurate wake results. The computational
domain exactly matched the test section as described in the invitation
document, i.e., 11.15 m long and 2.71 m wide and the wind tunnel walls were
included as no-slip wall boundaries.

As inflow the given analytical mean velocity profile ${U}_{\mathrm{inlet}}={u}_{\mathrm{ref}}\cdot {\left(y-{y}_{\mathrm{ref}}\right)}^{\mathit{\alpha}}$ was used. Furthermore, the synthetic eddy method was used to superpose time-dependent eddies with the characteristic length scale of 10 mm, and a turbulence intensity TI =5 %. All cases were run for 1.6 s to establish the flow prior to sampling, and then mean values were sampled over a period of 2 to 3 s. An example using STAR-CCM+ can be found in Mendonça et al. (2012).

POLIMI submitted a LES that was computed using the ALEVM code. It is an aerodynamic turbine simulation tool written in C++ and based on pisoFoam, which is an incompressible transient solver included in the OpenFOAM framework. The standard PISO (Pressure-Implicit with Splitting of Operators) solver was modified to include the effect of the turbine blades that are represented using the lifting line approach. The blade lines are discretized in segments based on the intersections with the numerical mesh grid, in which an actuation point acts on each segment. Each point of the actuator line (ACL) acts as an isolated blade section. More information about the ACL method can be found in Sørensen and Shen (2002). The wind velocity is numerically sampled for every blade point and used to compute the relative wind speed and the angle of attack. Thereafter, the aerodynamic forces are obtained through a look-up table, in which the blades' geometrical and aerodynamic properties are listed. Dynamic stall effects are not considered. In ALEVM the wind velocity is not sampled on a single point but averaged over a line, which is placed upstream of the blade point position with a distance proportional to the mesh cell dimension. The wind velocity is estimated using the mean of the velocity probed across the line. The main purpose of the relative wind speed estimation is in the angle of attack calculation. The wind velocity direction is then corrected to account for the local upwash due to the lifting line force. Based on the lifting line approach, the ALEVM code includes the turbine blade effect as an external momentum source term in the Navier–Stokes equations solved by the PISO algorithm.

ALEVM employs the well-known solution of the regularization kernel, smearing
the line forces on the multiple cells following a Gaussian distribution and
thus avoiding abrupt variation in the source term strength between adjacent
cells. The turbulence in the wake region is modeled using a LES, adopting the
Smagorinsky subgrid-scale model. For the time discretization scheme a
first-order implicit approximation is used, while the divergence
discretization scheme and the gradient discretization scheme are approximated
by second order. The simulation is run for a time interval of 20 s, while a
time step of $\mathrm{1.0}\times {\mathrm{10}}^{-\mathrm{3}}$ s is used. This results in an angular
rotation of about 2.4^{∘} per time step, which conversely means that 150
time steps make a full rotation. The resultant maximum Courant number of 0.21
is well below 1, indicating a sufficient temporal accuracy. The wind tunnel
walls are included as no-slip boundaries, while the inlet turbulence grid is
also geometrically modeled. The total cell count for the simulations is
approximately 4.1×10^{6}. Further details about the code can be found
in Schito and Zasso (2014).

UdelaR submitted another LES using their in-house developed caffa3d code. It
is an open-source, finite volume code, with second-order accuracy in space
and time, and parallelized with a message passing interface (MPI), in which
the domain is divided into unstructured blocks of structured grids. Complex
geometries are represented by a combination of body-fitted grids and the
immersed boundary method over both Cartesian and body-fitted grid blocks. The
code is F90 and currently runs on CPU, although a CUDA GPU version is
currently being developed. The properties of the geometry and the flow are
expressed as primitive variables in a Cartesian coordinate system, using a
collocated arrangement. An ACL approach is used to discretize the turbine
blades in the simulations. The aerodynamic forces on the blade elements are
computed using the provided XFoil data, and dynamic stall effects are not
considered. The forces, then, are projected onto the computational domain. In
order to compute the additional source term, a Gaussian smearing function is
used, taking into account one smearing factor for each direction: normal,
tangential, and radial to the rotor plane. The domain, representing the wind
tunnel ($\mathrm{12.5}{D}_{\mathrm{LARS}\mathrm{1}}\times \mathrm{3}{D}_{\mathrm{LARS}\mathrm{1}}\times \mathrm{2}{D}_{\mathrm{LARS}\mathrm{1}}$), is uniformly divided into $\mathrm{192}\times \mathrm{72}\times \mathrm{48}$ grid
cells in the streamwise, spanwise, and vertical directions, resulting in a
total cell count of approximately 0.7×10^{6}. A zero velocity gradient
is imposed at the outlet, while a logarithmic law is used to compute the
stress at the bottom wall and the symmetry boundary condition is used at the
lateral and top boundaries. An implicit Crank–Nicolson time scheme is used
with a time step of $\mathrm{2.5}\times {\mathrm{10}}^{-\mathrm{3}}$ s, that corresponds to 0.16 of the
rotor period (similar temporal resolution as used before, see for instance
Guggeri et al., 2017). Both time step size and spatial resolution were
defined based on previous simulations performed by UdelaR, particularly of
Blind test 4. The scale-dependent dynamic Smagorinsky model is used to
compute the subgrid-scale stress, using a local averaging scheme. The inflow
condition is obtained from a precursor simulation with a similar numerical
setup, but without model wind turbines and using a periodic boundary
condition at the west and east boundaries with a constant pressure gradient
as forcing term. The upstream model wind turbine is placed
2*D*_{LARS1} from the inlet boundary for test cases 1 and 2, while for
test case 3 the model wind turbine is placed 5*D*_{LARS1} from the
inlet boundary. UdelaR results are obtained after averaging the simulated
data over 52.5 s for test cases 1 and 2 and 67.5 s for test case 3. More
information about the application of caffa3d for wind energy simulations can
be found in Guggeri et al. (2017), Mendina et al. (2014), and Usera et al. (2008).

A third LES was submitted by KTH. The spectral element code Nek5000
(Fischer et al., 2008), which was developed to solve the dimensionless,
incompressible Navier–Stokes equations, was used. Each spectral element is
discretized using Gauss–Lobatto–Legendre quadrature points on which the
solution is expanded using Legendre polynomials. The LES applies a spatial
filtering technique to the two highest modes to remove a part of the energy
in the smallest scales and redistribute it to the lower modes thus
stabilizing the numerical simulation. The domain is discretized using
7.98×10^{4} uniformly distributed spectral elements with ninth-order
polynomials in each element, resulting in a total cell count of approximately
58×10^{6}. The numerical domain size corresponds to the dimensions of
the wind tunnel. In the case of the NTNU turbine this mesh size corresponds
to 45 grid points along each blade, when the blades are aligned with the
mesh. The distance between the inlet and the first turbine is 4 rotor radii
and the total length of the domain corresponds to 25 rotor radii. The
dimensionless time step used to advance the simulation is ${\mathit{\delta}}_{t}=\mathrm{1.5}\times {\mathrm{10}}^{-\mathrm{3}}$, which corresponds to 0.1432 % of a rotor revolution
and is chosen to satisfy the Courant–Friedrichs–Lewy condition. The wind
turbine blade geometry is represented by body forces according to the ACL
method with the lift and drag forces being computed using tabulated airfoil
data. For the NTNU turbines the experimental airfoil data set from DTU
(Sarlak et al., 2018) is used. It provides lift and drag coefficients over a
range of Reynolds numbers. The ForWind turbine lift and drag forcing was
computed using airfoil polars generated by XFoil that were provided in the invitation. Dynamic stall is not
considered in the modeling approach. At the blade tips the Prandtl tip
correction is applied. The forces computed at each actuator line are
distributed using a three-dimensional Gaussian distribution. The Gaussian
width is selected to be 2.5 times the average grid spacing. A mesh
independency study of the non-yawed NTNU wind turbine
established that using the aforementioned domain resolution combined with
this Gaussian width provided a converged averaged wake development. The tower
is also modeled using a body force approach. Both an oscillating lift
component and a constant and oscillating drag component are included. The
lift and drag coefficients for the mean drag and root-mean-squared lift and
drag of a cylinder are taken from Summer and Fredsøe (2011). The line forces are
then distributed using the three-dimensional Gaussian approximately in the
volume occupied by the tower. This setup has been previously validated
against experimental data from the NTNU turbine (Kleusberg et al., 2017). In the
case of the ForWind turbine only the actual tower of the support structure is
included. The turbulence at the inlet is modeled using sinusoidal modes with
random phase shifts and they are scaled with a von Kármán energy
spectrum. It is superimposed onto the desired uniform inflow condition. The
turbulence is calibrated to give a turbulence intensity at hub height of
approximately TI =10.0 % at the upstream turbine LARS1 and TI =4.8 % at the downstream turbine T2. At the outlet a zero-stress boundary
condition is used while the symmetry boundary condition is imposed laterally
to avoid resolving the wall boundary layer. More details about the
computational setup can be found in Kleusberg et al. (2017). The velocity and
TKE in the wake were temporally averaged over a dimensional time interval
Δ*t*= 4–5.3 s, which corresponds to over three flow-throughs of the
numerical domain in the NTNU cases.

The modelers were asked to predict the power coefficients *C*_{P}
(Eq. 2), where *P* is the mechanical power of the turbine, *ρ*
is the air density, and *A* the rotor swept area, as well as the thrust
coefficients *C*_{T} (Eq. 3), where *T* is the thrust force
acting on the whole test rig, including rotor and tower, perpendicular to the
rotor plane. Furthermore, the normalized yaw moments ${M}_{y}^{*}$
(Eq. 4) were required, where *M*_{y} is the yaw moment that is
calculated by a moment equilibrium of the horizontal forces taking the
distances of the load cells according to the center of the rotor plane into
account. In test case 1 the power coefficient *C*_{P, LARS1}, the
thrust coefficient *C*_{T, LARS1}, and the normalized yaw moment
${M}_{y,\phantom{\rule{0.125em}{0ex}}\mathrm{LARS}\mathrm{1}}^{*}$ are compared. For the aligned turbine array in
test case 2, the predictions for the upstream turbine are similar to test
case 1. However, additional predictions of *C*_{P, T2},
*C*_{T, T2}, and ${M}_{y,\phantom{\rule{0.125em}{0ex}}\mathrm{T}\mathrm{2}}^{*}$ for the downstream turbine
were compared. Due to a high uncertainty in the power and thrust force
measurements of the ForWind turbine, *C*_{P, ForWind},
*C*_{T, ForWind}, and ${M}_{y,\phantom{\rule{0.125em}{0ex}}\mathrm{ForWind}}^{*}$ are not compared
in test case 3. The performance characteristics of the NTNU turbines are
listed in Table 1.

$$\begin{array}{}\text{(2)}& {\displaystyle}& {\displaystyle}{C}_{\mathrm{P}}={\displaystyle \frac{\mathrm{2}P}{\mathit{\rho}\cdot A\cdot {u}_{\mathrm{ref}}^{\mathrm{3}}}},\text{(3)}& {\displaystyle}& {\displaystyle}{C}_{\mathrm{T}}={\displaystyle \frac{\mathrm{2}T}{\mathit{\rho}\cdot A\cdot {u}_{\mathrm{ref}}^{\mathrm{2}}}},\text{(4)}& {\displaystyle}& {\displaystyle}{M}_{y}^{*}={\displaystyle \frac{{M}_{y}}{\mathit{\rho}\cdot A\cdot {u}_{\mathrm{ref}}^{\mathrm{2}}\cdot D}}.\end{array}$$

The modelers were asked to provide predictions of the velocities and TKE in
full wake planes in the ranges $-\mathrm{1.0}\le z/D\le +\mathrm{1.0}$ and $-\mathrm{0.8}\le y/D\le +\mathrm{0.8}$, respectively. The grid points are separated by 0.1*D* resulting in a
grid consisting of 357 points, which is sketched in Fig. 5.
The time-averaged streamwise and vertical velocities, *u* and *v*, for all
points are normalized by *u*_{ref} so that ${u}^{*}=u/{u}_{\mathrm{ref}}$
and ${v}^{*}=u/{u}_{\mathrm{ref}}$, respectively. The same procedure is applied
for the TKE *k*, which is normalized to ${k}^{*}=k/{u}_{\mathrm{ref}}^{\mathrm{2}}$. The TKE
in a three-dimensional flow is defined as

$$\begin{array}{}\text{(5)}& {\displaystyle}k=\mathrm{1}/\mathrm{2}\left(\stackrel{\mathrm{\u203e}}{u{{}^{\prime}}^{\mathrm{2}}}+\stackrel{\mathrm{\u203e}}{v{{}^{\prime}}^{\mathrm{2}}}+\stackrel{\mathrm{\u203e}}{w{{}^{\prime}}^{\mathrm{2}}}\right).\end{array}$$

However, in the experiments only the two velocity components *u* and *v* were
measured. Comparing *u*^{′} and *v*^{′} showed that the TKE is not perfectly
isotropic. Therefore, additional measurements of the third velocity component
*w* for one wake scan were performed to investigate whether the fluctuations
*v*^{′} and *w*^{′} were in the same range. The results confirmed the assumption,
allowing an approximation of the TKE as

$$\begin{array}{}\text{(6)}& {\displaystyle}k=\mathrm{1}/\mathrm{2}\left(\stackrel{\mathrm{\u203e}}{{{u}^{\prime}}^{\mathrm{2}}}+\mathrm{2}\stackrel{\mathrm{\u203e}}{{{v}^{\prime}}^{\mathrm{2}}}\right).\end{array}$$

Two-dimensional wake contours are difficult to compare quantitatively as they cannot be plotted in the same diagram. However, they provide valuable insight into the shape and position of the wake. Therefore, the wake shapes are in a first iteration compared qualitatively. To obtain quantitative measures of comparison, different methods to compute the wake position, the energy content in the wake, and the magnitudes of the wake parameters are applied. These are described below.

In order to quantify the wake deflection, a method approximating the available power is used, which was previously described by Schottler et al. (2017). This method is deemed to be an appropriate approach to analyze the wake deflection of a yawed wind turbine as it takes the full wake scans into account. To find the wake center deflection, an imaginary rotor is laterally traversed in the wake while the wake center is defined as the position where the available power in the wake is the lowest. To get information about the energy content in the wake, the minimum of available power of the deflected wake is normalized by the available power found in the free stream of the experiment. With the resulting normalized minimum available power (${P}_{\mathrm{wake}}^{*}$), possible deviations in the location and magnitude of the energy content can be directly quantified.

From the statistical error measures proposed by Chang and Hanna (2004) the
normalized mean square error (NMSE) and the correlation coefficient (*r*) are
used to quantify the differences between simulations and experiments
regarding *u*^{*}, *v*^{*}, and *k*^{*}. For this purpose, all 357 points in
the *y*–*z* plane
of the CFD predictions are compared to the corresponding measurement points.
Perfect predictions would result in NMSE =0.0 and *r*=1.0. They are
calculated according to

$$\begin{array}{}\text{(7)}& {\displaystyle}& {\displaystyle}\text{NMSE}={\displaystyle \frac{\stackrel{\mathrm{\u203e}}{{\left({x}_{\mathrm{e}}-{x}_{\mathrm{s}}\right)}^{\mathrm{2}}}}{\stackrel{\mathrm{\u203e}}{{x}_{\mathrm{s}}}-\stackrel{\mathrm{\u203e}}{{x}_{\mathrm{e}}}}},\text{(8)}& {\displaystyle}& {\displaystyle}r={\displaystyle \frac{\stackrel{\mathrm{\u203e}}{\left({x}_{\mathrm{e}}-\stackrel{\mathrm{\u203e}}{{x}_{\mathrm{e}}}\right)\cdot \left({x}_{\mathrm{s}}-\stackrel{\mathrm{\u203e}}{{x}_{\mathrm{s}}}\right)}}{{\mathit{\sigma}}_{{x}_{\mathrm{e}}}\cdot {\mathit{\sigma}}_{{x}_{\mathrm{s}}}}},\end{array}$$

where *x*_{e} represents the experimentally measured values and
*x*_{s} are the simulated values. $\stackrel{\mathrm{\u203e}}{x}$ indicates the average
of all 357 points of the full wake scans. The standard deviation of all
points of the whole wake scan is given in *σ*_{x}. NMSE is a measure of
mean relative scatter and thus reflects both systematic and random errors
(Chang and Hanna, 2004); as the difference of every data point is squared, outliers
are emphasized, which is not considered to be significant as no major
outliers are expected. NMSE is used to analyze the predictions of *u*^{*} and
*k*^{*}. The method is, however, not suited to evaluate the discrepancy of
*v*^{*}, because *v*^{*} fluctuates around 0. Consequently the denominator of
Eq. (7) also ranges around 0, which results in unrealistically
high values for the NMSE. The correlation coefficient *r* represents a linear
relationship between the measurements and predictions. It directly compares
the measured and predicted values at a certain point. The predictions of all
three investigated wake properties *u*^{*}, *v*^{*}, and *k*^{*} are analyzed
using the coefficient *r*.

4 Results

Back to toptop
The results of *C*_{P, LARS1}, *C*_{T, LARS1}, and
${M}_{y,\phantom{\rule{0.125em}{0ex}}\mathrm{LARS}\mathrm{1}}^{*}$ for test case 1, in which the turbine is
operated at $\mathit{\gamma}=\mathrm{30}{}^{\circ}$, are depicted in
Fig. 6. For *λ*=6 the differences between the
experimental and numerical results are summarized in
Table 3. Comparing the values of *C*_{P, LARS1} in
Fig. 6a it can be seen that the simulation results
deviate from the measurements by up to 19 %. This is a larger scatter
compared to the previous blind tests, e.g., Bartl and Sætran (2017). However, it
should be kept in mind that the complexity is increased by the yawed turbine
operation. Siemens, who fully resolved the rotor, overpredict
*C*_{P, LARS1} by 14.2 %, which is almost in the same range as
UdelaR and POLIMI who used ACL with the provided polars from XFoil and showed
deviations of 18.5 % and 16.8 %, respectively. KTH also applied an
ACL model, but used the experimentally generated data set of airfoil polars
from DTU (Sarmast and Mikkelsen, 2012). Using these data results in a good agreement
with the experimental data with only a slight underprediction of 2.3 %.

The blade element momentum (BEM) tool Ashes (Thomassen et al., 2012) was used to analyze the blade
loads. The calculations showed that the angle of attack for the yawed
turbine, which is defined similar to two-dimensional conditions as the angle
between relative wind direction and the blade chord, is fluctuating
approximately 2.0^{∘} during one rotation in the outer third of the
blade, causing very high angles of attack. Note that the definition of the
angle of attack is herein based on a simplified two-dimensional analysis,
which omits the lateral component in the relative velocity during yaw. From
Fig. 2, it can be seen that the lift and drag coefficients
from the DTU experiments and XFoil are very different for such high angles of
attack. The experimental polars from DTU seem to be more accurate as the
polars predicted with XFoil for such high angles of attack, which explains
the better predictions of *C*_{P} by the simulations using the
experimental polars.

The thrust coefficients *C*_{T, LARS1} for the single yawed turbine
LARS1 are presented in Fig. 6b and only show a small
scatter of up to 7.0 % around the experimental results and thus are
almost all within the measurement uncertainty. Consequently, for
*C*_{T} predictions the experimental polars do not yield better
results with respect to the polars generated by XFoil. The yaw moment
${M}_{y,\phantom{\rule{0.125em}{0ex}}\mathrm{LARS}\mathrm{1}}^{*}$ is presented in Fig. 6c,
over a range of yaw angles from $\mathit{\gamma}=-\mathrm{40}$^{∘} to $\mathit{\gamma}=+\mathrm{40}$^{∘}. All simulations underestimate the experimental value of
${M}_{y,\phantom{\rule{0.125em}{0ex}}\mathrm{LARS}\mathrm{1}}^{*}$ while the deviations ranging from about 30 %
to 80 % are rather large. Nevertheless it should be kept in mind that the
values of ${M}_{y,\phantom{\rule{0.125em}{0ex}}\mathrm{LARS}\mathrm{1}}^{*}$ are very small and thus small
deviations result in large differences in percentage.

Figure 7 shows a comparison of the predictions of the
time-averaged streamwise velocity *u*^{*} at *x*=3*D*, with line profiles at
hub height added to the full wake contours. The wake contours as presented in
Fig. 7b show a slightly curled wake shape. The curled wake
shape was shown to develop from a counter-rotating vortex pair, as discussed
in detail by Schottler et al. (2018a) and Bartl et al. (2018b) for the same
experimental data set. Similar flow physics behind a yawed turbine were
observed in simulations by a full-scale turbine by Howland et al. (2016) and
Vollmer et al. (2016). The wake shape is generally well predicted by three of
the simulations. Only the wake predicted by UdelaR has a rather oval shape.
As expected, the wake is not only curled but also clearly deflected in the
negative *z* direction. This is very well predicted by all the simulations.
POLIMI and KTH match the deflection, whereas UdelaR and Siemens slightly
underestimate it. This is not consistent with the predictions of
*C*_{T} in which all institutions except Siemens estimate a lower
*C*_{T}. The tower shadow is also clearly visible in all simulations.
By fully resolving the rotor and turbine geometry Siemens matches the
experimental results almost perfectly. UdelaR and KTH, who both modeled tower
and nacelle with a line of drag forces, simulate a fairly accurate tower
shadow. Even though POLIMI did not model nacelle and tower, their results
show a strong velocity deficit in the area where the tower shadow is
expected. This effect is considered to be caused by the flow velocities
modeled near the wind tunnel floor, whose influence is pronounced in all
simulations by POLIMI. In the free stream, the shear flow can be clearly seen
in the experimental results. Siemens, UdelaR, and KTH apply a user-defined
shear function at the inlet and thus predict a smooth shear profile, while
POLIMI, who fully resolved the turbulence grid at the inlet, simulate a shear
profile with a too strong shear and very low velocities close to the floor.
Figure 7a shows that POLIMI generally predicts lower velocities
in the free stream, as the normalized velocity *u*^{*} at hub height does not
reach 1.0 in the free stream. Nevertheless, the velocities behind the rotor
are represented very well, while a poor NMSE_{u} of 0.017 and a *r*_{u} of
0.878 show the discrepancy in the free stream to the measurements. All in
all, it can be seen that *u*^{*} is predicted well by all simulations.
Siemens' results for this test case are almost perfectly in accordance with
the experiments, which results in a very low NMSE_{u} of 0.002 and a large
*r*_{u} of 0.964. Good statistical performance values are also achieved by KTH
(NMSE_{u}=0.002, *r*_{u}=0.957), even though the velocity deficit in the
wake center is slightly underestimated. An even clearer underprediction of
the velocity deficit in the wake center can be observed for the UdelaR
simulations, which result in a NMSE_{u} of 0.005 and a *r*_{u} of 0.914. These
observations are confirmed by comparing the available power levels in the
wake (Table 4). In the case of Siemens' accurate simulations
of *u*^{*}, ${P}_{\mathrm{wake}}^{*}$ only deviates by −2.7 % from the
experiments. UdelaR underestimates the velocity deficit in the center
significantly, resulting in an overprediction of ${P}_{\mathrm{wake}}^{*}$ by
42.7 %. KTH also overestimates ${P}_{\mathrm{wake}}^{*}$ by 15.6 %, which
confirms the higher velocities observed in the wake center. The available
power method shows a good agreement of POLIMI's simulations with the
experiments, deviating only 11.2 %. This is because the method takes only
the area in the wake center into account and thus is not affected by the
deviating velocity levels in the free stream.

Next, Fig. 8 shows the normalized vertical flow component
*v*^{*}. In general the velocity contours are dominated by two major flow
patterns: a larger-scale dipole, characterized by flow from the ceiling to the center (${v}^{*}<\mathrm{0}$) and from the bottom to the center (${v}^{*}>\mathrm{0}$); and a smaller dipole at the rotor edge at $z/D=-\mathrm{0.8}$, where *v*^{*}
is positive outside the rotor swept area and negative in the rotor swept area
featuring strong gradients between the peaks. These structures are generally
predicted fairly well. Siemens, POLIMI and KTH match the flow pattern very
accurately, which is confirmed by the line plots at hub height
(Fig. 8a). High values of the correlation coefficient *r*_{v} for
these three simulations range from 0.819 to 0.866 and confirm the
observations. The simulation by UdelaR (Fig. 8e) does not show
very strong gradients and thus does not capture the detailed flow patterns.
This is assumed to be due to a rather coarse mesh resolution for this
simulation and can be seen in the low *r*_{v} value of 0.383. Nevertheless,
the general shape showing the large-scale structures on the right is captured
well.

The normalized TKE *k*^{*} is presented in Fig. 9. The contours
show a clear ring of turbulence located around the rotor area. Similar to the
shape of *u*^{*} the ring is slightly compressed at the right side.
Figure 9a shows that all simulations predict the position and
magnitude of the turbulence peaks very well. Larger differences between
measurement and simulations can be found outside of the ring. Here, Siemens
predicts a very low TKE close to ${k}^{*}=\mathrm{0}$ in the free stream and in the
wake center. This underprediction of *k*^{*} is assumed to be due to the
rather large cell size in the free stream that is too coarse to sustain the
free stream turbulence. It results in a rather large NMSE_{k} of 0.663,
whereas *r*_{k} with 0.873 suggests a good correlation of the shapes. POLIMI's
prediction of *k*^{*} shows a higher background turbulence, especially below
the rotor area in the positive *z* direction. These discrepancies result in
poor statistical performance values of NMSE_{k}=0.332 and *r*_{k}=0.583.
UdelaR's results show a clear shear profile of *k*^{*} with increasing
turbulence towards the wind tunnel floor. This is quite different from the
experimental results; therefore, the values of NMSE_{k}=1.045 and *r*_{k}=0.333 are observed to be far off. The simulations of KTH are in very good
agreement with the experiments which is confirmed by a low NMSE_{k} of 0.085
and high *r*_{k} of 0.924.

The comparisons of *u*^{*}, *v*^{*}, and *k*^{*} 6*D* behind LARS1 show
similar trends as already observed at a distance of 3*D*. Therefore, the
results at 6*D* are not shown. The comparison parameters summarized in
Table 4 confirm these observations. A major difference to the
wake at 3*D* is a more distinct curled wake shape, which is generally well
predicted by all simulations. The wake is further deflected, while the skew
angle is lower compared to the observations at *x*=3*D*
(Table 4). This is expected to be due to the large blockage
ratio of the NTNU turbine and the interference of the wake with the wind
tunnel walls. The experimental results of the wake at *x*=6*D* are also
documented by Bartl et al. (2018b).

In test case 2 an aligned turbine array with both NTNU turbines LARS1 and T2
is investigated. The upstream turbine LARS1 is operated at
*γ*_{LARS1}=30^{∘} and *λ*_{LARS1}=6.0.
Consequently, *C*_{P, LARS1}, *C*_{T, LARS1}, and
${M}_{y,\phantom{\rule{0.125em}{0ex}}\mathrm{LARS}\mathrm{1}}^{*}$ are identical to test case 1
(Fig. 6, Table 3) and are therefore
not further discussed here. The downstream turbine T2 is operated at
*γ*_{T2}=0^{∘} and *λ*_{T2}=5.0. The tip
speed ratio *λ*_{T2}=5.0 is computed using the far-upstream
reference velocity *u*_{ref}=10.04 m s^{−1}. T2 is located 3*D*
behind the yawed upstream turbine, meaning that the wake flow of test case 1
represents the inflow for T2. Detailed results of power, thrust, and yaw
moments for the upstream and downstream turbine operated at different yaw
angles, separation distances, and inflow conditions are presented by
Bartl et al. (2018a). Previous blind tests discussed the higher spread in
prediction results of a downstream turbine's performance. This is confirmed
by comparing *C*_{P, T2}, *C*_{T, T2}, and
${M}_{y,\phantom{\rule{0.125em}{0ex}}\mathrm{T}\mathrm{2}}^{*}$ of T2, which show a significantly larger spread of
performance than for test case 1 (Fig. 10,
Table 3). The simulation results of the downstream turbine's
power coefficient *C*_{P, T2} (Fig. 10a) deviate
between 0 % and 48.9 % from the experimental results. KTH matches the
experimental value exactly and thus confirms the good forecast from test case
1. Siemens predicts the available power in the wake fairly accurately and
thus overestimates *C*_{P, T2} by only 10.5 %. POLIMI and UdelaR
over estimate *C*_{P, T2} significantly by 43.6 % and 48.9 %,
respectively. This trend could already be seen for the upstream turbine power
coefficient *C*_{P, LARS1} and is enhanced by overpredicting the
available power in the wake for UdelaR. POLIMI prognosticates less available
power in the wake. The simulation results of the downstream turbine thrust
coefficient *C*_{T, T2} (Fig. 10b) show smaller
deviations than those for *C*_{P, T2}. Nevertheless, they are
slightly larger than those of *C*_{T, LARS1} in test case 1. All
simulations underestimate *C*_{T, T2} while KTH's result shows the
largest deviation of −15.3 % compared to their accurate prediction of
*C*_{P, T2}. Siemens and UdelaR show a similar thrust that deviates
from the experimental value by −10.7 % and −10.6 %, respectively.
POLIMI underpredicts *C*_{T, T2} by 4.6 %. A larger spread is
again observed for the simulations of ${M}_{y,\phantom{\rule{0.125em}{0ex}}\mathrm{T}\mathrm{2}}^{*}$
(Fig. 10c) as the values for ${M}_{y,\phantom{\rule{0.125em}{0ex}}\mathrm{T}\mathrm{2}}^{*}$ are
very small and consequently more difficult to predict. Siemens and POLIMI are
observed to overestimate ${M}_{y,\phantom{\rule{0.125em}{0ex}}\mathrm{T}\mathrm{2}}^{*}$ by 101.4 % and
43.3 %, respectively. UdelaR underpredicts ${M}_{y,\phantom{\rule{0.125em}{0ex}}\mathrm{T}\mathrm{2}}^{*}$ for
50.6 % while KTH matches the experimental results very accurately with
only 1.5 % difference.

This section discusses the wake characteristics 3*D* behind the two-turbine
array. The wake is clearly deflected in the negative *z* direction. However,
the deflection is not as big as 6*D* behind the single yawed turbine, but
rather in the same range as 3*D* behind the single yawed turbine. These
results compare well with a recent LES study by Fleming et al. (2018), who
simulated a similar wake deflection behind a non-yawed downstream turbine
exposed to a partial wake inflow. This suggests that a further wake
deflection is restricted by the non-yawed downstream turbine and maintained
at approximately the same level at which it hits the downstream turbine.
Moreover, the wake shape does not show a curled shape, instead being rather
oval (Fig. 11). The tower shadow, which is mainly formed by the
T2 downstream turbine tower, is more centered than in test case 1 and is well
predicted in all simulations. The shear profile in the free stream is well
captured by all simulations. However, all predictions show a slightly lower
velocity level than in the experiment. POLIMI's simulations indicate a rather
strong velocity gradient again, with very low velocities close to the wind
tunnel floor. However, the gradient is better established than in test case 1
as it develops further downstream. The line plot in Fig. 11a
confirms that all the simulations underestimate the additional speed-up
around the downstream turbine rotor. Siemens overpredicts the velocity
deficit in the wake center which is confirmed by the available power that is
19.5 % lower as the one resulting from the experiments. Considering the
whole wake scan, the statistical performance parameters NMSE_{u}=0.006 and
*r*_{u}=0.976, on the other hand suggest better agreement. POLIMI predicts
the velocities in the wake very accurately and estimates
${P}_{\mathrm{wake}}^{*}$ only 12.1 % lower than in the experiments. The
statistical measures, however, do not confirm the good match of the energy
level, resulting in a NMSE_{u} of 0.025 and a *r*_{u} of 0.925. The too low
velocities in the free stream, which are not considered in
${P}_{\mathrm{wake}}^{*}$, are deemed to impair the correlation coefficients
here. The available power of UdelaR exceeds that of the experiments clearly
by 51.1 %, which is mainly due to an underprediction of the velocity
deficit in the wake center. Nevertheless, the statistical parameters that
take the whole measurement grid into account, suggest a good agreement with
NMSE_{u}=0.010 and *r*_{u}=0.928 as the lower velocities in the free
stream counterbalance the higher velocities in the wake center. The velocity
levels in the wake center are overpredicted by KTH; however, the available
power is in good agreement with the experiments and only deviates 4.1 %.
This is confirmed by good statistical values of NMSE_{u}=0.007 and *r*_{u}=0.976. The wake deflection is predicted well by all simulations. POLIMI
and KTH match it accurately, whereas Siemens underpredicts it by $z/R=\mathrm{0.041}$ and UdelaR by $z/R=\mathrm{0.082}$.

The contours of the vertical velocity component *v*^{*} behind the turbine
array show a similar flow pattern as the one behind the single yawed turbine
(Fig. 12). Nevertheless, the magnitudes of *v*^{*} are smaller
compared to test case 1. The flow pattern is described fairly accurately by
all simulations. However, Siemens, POLIMI, and KTH have average correlation
values *r*_{v} ranging from 0.452 to 0.586. The predictions by UdelaR are again
rather coarse and thus reveal less details, which results in an even lower
linear correlation coefficient of only *r*_{v}=0.091.

The TKE *k*^{*} in the wake behind the turbine array as shown in
Fig. 13 is characterized by a ring of higher TKE that is
deflected in the same way as *u*^{*} and thus is similar to test case 1.
Compared to the single turbine wake, the ring of high TKE is observed to be
broader and flattened out (Fig. 13a). The peak locations are
prognosticated very well by all simulations. However, Siemens and KTH
underpredict the levels of *k*^{*}, while UdelaR overpredicts the turbulence
in the ring, especially on the right hand side of the wake. POLIMI seems to
match the turbulence in the ring fairly accurately which results in a low
NMSE_{k} of 0.087 and *r*_{k} of 0.915. Good *r*_{k} values are also
obtained by Siemens and KTH with *r*_{k}=0.947 and *r*_{k}=0.976,
respectively. However, their NMSE_{k} values of NMSE_{k}=0.345 and
NMSE_{k}=0.153, respectively, suggest some deviations. The overprediction
of TKE by UdelaR results in slightly poorer statistical performance values of
NMSE_{k}=0.709 and *r*_{k}=0.784.

In the third test case the wake behind the yawed ForWind turbine is
investigated. It was simulated by three of the modelers, while POLIMI did not
submit predictions for this test case. The contours of the streamwise
velocity 3*D* (*D*=*D*_{ForWind}) behind the ForWind turbine are
presented in Fig. 14b–e. They show a more distinct curled wake
shape than that observed for the NTNU turbine. In contrast to the NTNU
turbine, the ForWind turbine rotates in a clockwise direction when observed
from upstream. A counterclockwise wake rotation deflects the wake center to
the lower half behind the rotor as described in detail by
Schottler et al. (2018a). Furthermore, it can be seen that due to the smaller
rotor diameter there is less blockage which reduces the
speedup around the rotor significantly (Fig. 14a). Thus, a
smooth shear profile is observed in the free stream. The velocity deficit as
well as the curled wake shape are predicted very well by all simulations with
only UdelaR's simulations showing a less distinct curl. The position of the
largest velocity deficit is consistent for all simulations. Nevertheless,
most participants overestimate the magnitude of the velocity deficit. Siemens
has the largest deviations from the experiments, which results in an
available power that is 49.4 % lower compared to the measurements.
However, when not only taking the imaginary rotor area into account but also
considering the whole wake scan, the statistical performance values NMSE_{u}=0.012 and *r*_{u}=0.968 indicate a good agreement. UdelaR predicts
velocities that result in only 27.6 % less available power for a
potential downstream turbine, but NMSE_{u}=0.007 and *r*_{u}=0.953 are in
the same range as the Siemens predictions and indicate a good match of the
whole wake scan. The KTH simulation matches the experimental results best and
shows the smallest deviation of available power and with NMSE_{u}=0.005 and
*r*_{u}=0.960 their statistical performance values confirm the good
agreement. The wake of the ForWind turbine is slightly more deflected than
3*D* behind the NTNU turbine (Table 6). Siemens again
underpredicts the deflection, whereas UdelaR and especially KTH predict a
stronger deflection of the wake than observed in the experiments.

The contours of the normalized vertical velocity *v*^{*}
(Fig. 15b–e) are similar to those observed 3*D* behind LARS1.
The flow field is dominated by the same major flow patterns as already
observed in test case 1. The major difference is that the peaks in the
positive *z* direction are more centered and that the dipole at the left
rotor edge is not as distinct. All simulations of *v*^{*} match the
experiment fairly accurately, which results in similar *r*_{v} values ranging
from 0.802 to 0.851. Siemens, however, predicts slightly higher positive
peaks, but the distribution of *v*^{*} is captured very well. The same
applies for KTH and UdelaR, who again predict smoother gradients due to a
coarse mesh resolution.

The TKE contours presented in Fig. 16b–e also indicate a clear
curled shape. The *k*^{*} values behind the ForWind turbine are observed to
result in a significantly wider peak in the positive *z* direction
(Fig. 16a) than observed behind LARS1. In contrast to the
previous test cases, *k*^{*} is distributed more smoothly over the wake which
results in higher turbulence levels in the wake center. The shape of the TKE
contours is accurately represented by all simulations. Siemens and UdelaR,
however, over estimate the peak magnitudes significantly, while Siemens
predicts the peak location in the upper half accurately. UdelaR's simulation
is observed to result in higher TKE values in the whole ring. The simulations
of KTH are in closest agreement with the experiments. The linear correlation
coefficients are in the same range (*r*_{k}=0.878–0.905) for all three
predictions. Larger deviations can be observed in NMSE_{k} that range from
0.202 to 0.734.

The comparison of the wake characteristics 6*D* behind the yawed ForWind
turbine results in conclusions similar to those at 3*D*. Therefore, the
figures comparing *u*^{*}, *v*^{*}, and *k*^{*} 6*D* behind the ForWind
turbine are not shown here, but the comparison parameters and statistical
performance measures are listed in Table 6. The streamwise
velocity *u*^{*} and the vertical velocity *v*^{*} are generally predicted
accurately, which is represented by better comparison parameters and
statistical performance values at 6*D* than at 3*D* for all simulations.

5 Discussion and conclusions

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The results of four different computational contributions were compared to experimental wind tunnel results in this blind test experiment. The modelers submitted predictions for the performance of two single yawed turbine models and an aligned turbine array where only the upstream turbine is yawed. Furthermore, they predicted the mean and turbulent wake flow behind two different model turbines and the turbine array.

The power of a single yawed turbine *C*_{P, LARS1} was predicted with
a scatter of ±19 %, which was slightly bigger than in the two
previous blind test experiments. A bigger scatter of ±49 % is
observed in the predictions of the power coefficient *C*_{P, T2} for
a downstream turbine operating in partial wake conditions of the yawed
upstream turbine. This variation is significantly larger than the scatter for
an aligned downstream turbine operated in a full wake in the Blind test 4
workshop (Bartl and Sætran, 2017), in
which a scatter of only ±15 % was observed for the same distance.
For a downstream turbine with a lateral offset operated in a partial wake in
Blind test 3 (Krogstad et al., 2015), however, a similar variation in power
prediction was observed (±50 %). These results indicate a more
difficult prediction of turbine performance for an operation in a partial
wake situation, due to the increased complexity of highly unsteady blade
loading over the course of a rotation.

The predictions of the thrust coefficients *C*_{T, LARS1} and
*C*_{T, T2} show a smaller scatter of ±7 % and ±15 %, respectively, which is in the same range as observed in the Blind
test 4 workshop. Consequently, the thrust predictions are not influenced as
strongly by yawing the turbine as the power predictions. Three of the
simulations modeled the rotor by an actuator line (AL) approach, two of which
used XFoil generated polars while one simulation used an experimentally
measured data set. The power, thrust, and yaw moment predictions of the
simulations using an experimental data set consistently performed best. As
the rotor was operated in yaw (test case 1) or a partial wake inflow (test
case 2), the angle of attack varied during one rotor rotation, reaching high
values. The experimental airfoil polars might be more realistic for such
large angles of attack, which result in better performance predictions. The
IDDES model fully resolved the rotor geometry and directly calculated the
forces on the rotor. The length of the simulation interval was chosen to be
rather short in order to save computational time. This might have influenced
the accuracy of the time-averaged blade forces. The parameters of the wake
flow, however, were not observed to be impaired by the short averaging
interval.

When comparing CFD predictions to experimental measurements it is important
to quantify the differences. Therefore, different techniques have been
applied to analyze the wake properties. The statistical methods NMSE and *r*
were in good agreement with each other and gave an acceptable indication of
how well the simulations performed. However, they analyzed the whole wake
scan and did not reveal specific discrepancies. The statistical methods were
not always in accordance with the available power method, which only
considered an area around the wake center for comparison. The available power
method thus provided a good quantification of the wake deflection and the
energy content in the wake. However, it only compared a certain section of
the wake scan and accordingly could not quantify the overall performance of
the simulations. Comparing the wake contours visually resulted in a
qualitative comparison, revealing flow patterns and differences in the wake
shape for each simulation in comparison to the experiments. Combining the
outcome from all methods provided a good overall picture of how well the wake
properties from CFD predictions and measurements agree.

The comparison of the mean streamwise velocity *u*^{*} in the wake generally
shows a very good agreement between the experimental data and the numerical
predictions. The general features such as the wake shape and deflection were
predicted well by all the simulations using IDDES as well as LES. The
velocity in the wake was also predicted fairly accurately by all simulations.
The high mesh resolution of the IDDES model by Siemens was seen to reveal
exact flow details and thus resulted in a high statistical correlation for
*u*^{*}. A similarly high statistical correlation was obtained by KTH's
*u*^{*} predictions using their LES-ACL simulation. The rather coarse mesh of
UdelaR saved computational time but also smeared flow details; nevertheless,
the velocity and turbulence levels were predicted accurately. Modeling the
grid at the inlet as done in POLIMI's simulation was observed to not
perfectly predict the inflow, which was not as smooth at the position of the
first turbine as in the measurements. Applying a user-defined shear profile
at the inlet, as performed by the other institutions, resulted in better
predictions of the free stream flow. Despite its low magnitude, the complex
patterns in vertical velocity component *v*^{*} were in general accurately
predicted by all simulations. The details of the flow were well captured by
both LES and IDDES models. One of the most positive results of this blind
test experiment were the very accurate predictions of the TKE in the wake
behind a single turbine and the two-turbine array. The prediction of wake
turbulence was seen to be difficult in previous blind test comparisons. This
workshop, however, confirms the strength of LES and IDDES simulations to
accurately predict rotor-generated turbulence.

Furthermore, the good results of the simulations based on a lower cell count indicate a new trend towards CFD codes that are able to perform accurate wake flow predictions at significantly lower computational cost. This becomes especially important for wake predictions of full-scale turbines in which the dimensions and Reynolds numbers exceed those of the experiments. Consequently, simulations with a fine grid may be very hard to realize in such a case. Nevertheless, the good performance of the coarse-grid simulations in the blind test shows that they are a promising tool for full-scale wake predictions.

Overall, the results of this blind test comparison confirm a continuous improvement in performance and wake flow predictions from Blind test 1 to Blind test 5. LES-ACL approaches as well as the hybrid IDDES technique were confirmed to be able to perform accurate predictions, also for complex setups featuring highly unsteady flow in yawed and partial wake operation.

Data availability

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Data availability.

All presented wake data in this paper is available at https://doi.org/10.5281/zenodo.1193656 (Schottler et al., 2018b).

Author contributions

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Author contributions.

FM, JS and JB planned the carried out the experiments. RF and SE carried out the simulations indicated as “Siemens”. LB and PS carried out the simulations indicated as “Polimi”. MD and AG carried out the simulations indicated as “UdelaR”. EK and DH carried out the simulations indicated as “KTH”. MH, JP, MA and LS initiated and supervised the project. The workshop was initiated and prepared by JB, FM, JS and LS. The data was post-processed and compared by FM. The manuscript was written by FM, and revised by JS and JB. The description of the simulation methods was provided by Siemens, Polimi, UdelaR and KTH. All authors provided critical feedback and contributed to the shape of the manuscript.

Competing interests

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Competing interests.

The authors declare that they have no conflict of interest.

Acknowledgements

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Acknowledgements.

The authors would like to thank Stefan Ivanell and the staff of the Wind
Energy group from Uppsala University and Campus Gotland for providing the
venue for the workshop.

Edited by: Alessandro Bianchini

Reviewed by: Gerard Schepers and one anonymous referee

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