This is a summary of the results of the fourth blind test
workshop that was held in Trondheim in October 2015. Herein, computational
predictions on the performance of two in-line model wind turbines as well as
the mean and turbulent wake flow are compared to experimental data measured
at the wind tunnel of the Norwegian University of Science and Technology (NTNU). A detailed description of the model geometry, the
wind tunnel boundary conditions and the test case specifications was
published before the workshop. Expert groups within computational fluid
dynamics (CFD) were invited to submit predictions on wind turbine
performance and wake flow without knowing the experimental results at the
outset. The focus of this blind test comparison is to examine the model
turbines' performance and wake development with nine rotor diameters
downstream at three different turbulent inflow conditions. Aside from a
spatially uniform inflow field of very low-turbulence intensity
(TI

Five different research groups contributed their predictions using a variety of simulation models, ranging from fully resolved Reynolds-averaged Navier–Stokes (RANS) models to large eddy simulations (LESs). For the three inlet conditions, the power and the thrust force of the upstream turbine is predicted fairly well by most models, while the predictions of the downstream turbine's performance show a significantly higher scatter. Comparing the mean velocity profiles in the wake, most models approximate the mean velocity deficit level sufficiently well. However, larger variations between the models for higher downstream positions are observed. Prediction of the turbulence kinetic energy in the wake is observed to be very challenging. Both the LES model and the IDDES (improved delayed detached eddy simulation) model, however, consistently manage to provide fairly accurate predictions of the wake turbulence.

Given the constraints of transmission and installation costs, the available area for offshore wind farm installations is fairly limited. Under these circumstances wake interactions play an important role when evaluating the energy production since the energy captured by an upstream wind turbine leaves significantly less energy in the wake for the downstream turbine. For certain wind directions these power losses are estimated to be up to 10–20 % for large offshore wind farms (Barthelmie et al., 2009). Furthermore, the rotor-generated turbulence in the wake is a source of augmented material fatigue on the downstream rotor.

In order to be able to come up with holistic control approaches for optimizing a wind farm, well-performing prediction tools for the wake flow behind a wind turbine rotor for all kinds of atmospheric conditions are needed. Therefore, the development of simple wake models already began in the early 1980s. Analytical wake models by Jensen (1983), Ainslie (1988), Crespo et al. (1988), Frandsen et al. (2006) and Larsen et al. (2008) are based on a number of simplifications and are calibrated with empirical parameters. Most of the state-of-the-art software used for industrial wind farm planning is still based on these engineering wake models. However, they are not able to reconstruct the wake characteristics in a sufficient degree of detail (Sanderse et al., 2011).

With an increase in computational power, advanced computational fluid dynamics (CFD) models based on more fundamental physics arose. These CFD models are computationally more expensive but are able to resolve the flow structures in much larger detail. In general, two types of CFD approaches are state of the art in wake modeling: Reynolds-averaged Navier–Stokes (RANS) equations that average the turbulent fluctuations and the computationally more expensive large eddy simulations (LESs), which solve for large eddies only. Hybrid models like detached eddy simulations (DESs) combine the advantages of calculating unsteady flow effects from LES as well as resolving small scales in the boundary layers like RANS does. Another challenge is the modeling of the interaction of the wind turbine rotor with the flow: the rotor geometry can either be fully resolved or simplified as a two-dimensional force field. The latter option is usually more efficient with respect to computational time. In RANS models it is possible to fully resolve the rotor geometry and thus model complex three-dimensional flow. In LES models, however, a full resolution of the rotor geometry is difficult because the smaller scales that determine the forces at the interaction surface are not resolved. Thus, the rotor is often modeled as a two-dimensional force field, which requires detailed knowledge of the lift and drag forces that act under certain inflow conditions.

Even though the wake behind full-scale wind turbines was recently measured (Kocer et al., 2011; Kumer et al., 2015; Trujillo et al., 2016), the unsteady inflow conditions in full-scale experiments make it very difficult to use those data to verify wake prediction models. Therefore, wind tunnel experiments on model turbines under controlled boundary conditions are an appropriate method for verifying simulation tools.

Despite the drawbacks of low Reynolds numbers and possible wall blockage
effects in model experiments, a number of well-defined comparison tests have
been conducted. One of the first model-scale experiments was the
investigation by Talmon (1985). The wake was measured on a small rotor with a diameter of

At the Norwegian University of Science and Technology (NTNU) two model
turbines of the rotor diameter

The largest rotor investigated for wake comparison studies was the MEXICO rotor, with a diameter of 4.5 m (Schepers et al., 2010), in which the rotor performance as well as the wake flow were examined in detail. A second campaign investigating even more effects, including span-wise pressure distributions, yaw misalignment and unsteady effects, was realized at a large German–Dutch Wind Tunnel (DNW). A benchmark comparison of the comprehensive set of measurement data with numerical calculations is found in Schepers et al. (2014).

NREL S826 airfoil geometry.

In 2011 the first blind test workshop on turbine performance and wake
development behind one model turbine was organized. The geometry of the
model turbine and wind tunnel environment was made available to the public,
and dedicated research groups were invited to predict the model turbine's
performance and the wake development up to

The experimental data of this study are measured in the closed-loop wind
tunnel at NTNU in Trondheim. The rectangular test section of the wind tunnel
is 2.71 m broad, 1.81 m high and 11.15 m long. The wind tunnel roof is
adjusted for a zero pressure gradient, generating a constant velocity in the
entire test section. The wind tunnel inlet speed is controlled by an inlet
contraction, which is equipped with static pressure holes at the
circumferences at two defined cross sections. The wind tunnel is driven by a
220 kW fan located downstream of the test section, able to generate
maximum wind speeds of up to

The model wind turbines have a three-bladed rotor with diameters of

The turbine blades were designed using the NREL S826 airfoil from the root
to the tip. The airfoil, as shown in Fig. 1, was designed at the National
Renewable Energy Laboratory (NREL) and a detailed description of the
airfoil's characteristics is given by Somers (2005). Herein, the geometry is
specified and the performance characteristics are estimated. Lift and drag
coefficients are presented for a range of operating Reynolds numbers
(

Setup of the model wind turbines in the wind tunnel and reference coordinate system.

Test case A: low-turbulence uniform inflow

Both rotors are designed for an optimum tip speed ratio of

In this blind test experiment the model turbines are positioned at the wind
tunnel center line. The upstream turbine T1's rotor plane is located at

For this blind test experiment three different turbulent inflow conditions are investigated. This is supposed to shed light on the effects of various turbulence levels, as well as shear in the atmosphere, on the performance of a wind turbine and its wake. As it is almost impossible to create realistic conditions that resemble atmospheric stability classes in a wind tunnel environment, simplified cases of turbulent inflow are created.

The first inflow condition investigated is a uniform inflow of very low
turbulence and is described from here on as test case A. As shown in Fig. 3a, there is no grid installed at the inlet of the test section, resulting in
a clean and uniform flow. Hot-wire measurements at the upstream turbine
position give a turbulence intensity level of TI

In order to investigate the effects of turbulence on wind turbine
performance and wake development, the measurements of test case B are
performed using a large-scale turbulence grid at the inlet to the test
section (Fig. 3b). The biplanar grid has a solidity of 35 % and is
built from wooden bars with a 47 mm

Measured and rotor-averaged values of normalized mean
velocity

In a third test case C, the effect of shear flow combined with high
turbulence is investigated. For this purpose a large-scale shear-flow-generating turbulence grid is installed at the inlet of the test section, as
shown in Fig. 3c. The horizontal mesh width is constant at

Because wind shear and turbulence are generated only at the grid position at the
tunnel inlet, their development throughout the tunnel is measured for
all turbine positions. Wind shear can be described by the power law in Eq. (

During the present experiments, the reference wind speed was kept constant at

For test case C, in which the velocity increases with height, the
reference velocity of

Both model turbines are equipped with a HBM torque transducer of the type T20W-N/2-Nm, which is connected to the rotor shaft through flexible couplings. In addition, an optical photo cell is installed on the shaft, giving a defined peak signal for every full rotation of the rotor. After subtracting the measured friction in the ball bearing between the rotor and torque sensor, the mechanical power in the rotor shaft can be calculated. The power in both turbines is measured and controlled simultaneously to ensure a stable operation of both turbines.

Overview of simulation methods and parameters. Abbreviations for rotor models: actuator line (ACL), blade element momentum (BEM), fully resolved rotor (FRR). Abbreviations for flow models: improved delayed detached eddy simulation (IDDES), large eddy simulation (LES), Reynolds-averaged Navier–Stokes simulation (RANS).

The thrust force is measured by a six-component force balance produced by Carl Schenck AG. The drag force on the tower and nacelle structure is first measured without the rotor being present. Thus, it is possible to assess the rotor thrust by subtracting the tower–nacelle drag from the total drag.

The mean and turbulent velocities in the wake behind the upstream turbine T1
are measured by a single hot-wire anemometer (HWA) in constant temperature
mode (CTA). Each measurement point is sampled for 45 s at 20 kHz, resulting in
a total of 9.0

The statistical uncertainty of every sample of the power, thrust and mean
velocity measurements is calculated following the procedure proposed by
Wheeler and Ganji (2004). Random errors are computed from the standard
deviations of the various measured signals on a 95 % confidence interval.
Also taking systematic errors from the calibration procedures into account
by following the procedure of Eriksen (2016), a total error is calculated.
Herein, the systematic error of about

The uncertainty in the upstream turbine power coefficient at design
conditions is calculated to be within

The computational methods applied by the five different contributors are described in the following subsections. Furthermore, an overview of the different simulation methods and parameters is presented in Table 1.

S. Sarmast, R. Mikkelsen and S. Ivanell from Uppsala University, Campus Gotland, Sweden, and Technical University of Denmark (DTU), Campus Lyngby, Denmark, contributed with a dataset simulated by LES methods combined with an ACL approach. The DTU in-house code EllipSys3D, which is based on a multi-block finite volume approach, was used to solve the Navier–Stokes computations. The convective terms are herein discretized by a combination of third-order and a fourth-order schemes. The resolution of the time domain is defined small enough, that a blade tip moves less than a half cell size per time step. The flow field around the wind turbine rotor was simulated using the actuator line technique developed by Sørensen and Shen (2002). Herein, the Navier–Stokes equations are solved with body forces distributed along rotating lines representing the blades of the wind turbine. The lift and drag coefficients are taken from the previously mentioned self-generated dataset for the NREL S826 airfoil by Sarmast and Mikkelsen (2013). For each of the 43 blade points the forces are interpolated for the local Reynolds numbers in a range of 40 000 to 120 000. Additionally, a force line is introduced to account for the drag force generated by the tower. The wake flow field is calculated by solving the Navier–Stokes equations using LES with an integrated sub-grid-scale (SGS) viscosity model.

A regular Cartesian grid, which is divided into 875 blocks, makes out the computational domain. With 32 points in each block and 43 points representing each blade, a total of 28.6 million mesh points are used to simulate the various test cases. This resolution was tested to give a grid-independent simulation result.

The inlet turbulence is modeled by implanting synthetically resolved
turbulent fluctuations 1.5

N. Stergiannis from Vrije University and Von Karman Institute (VKI) in Brussels, Belgium,
performed Reynolds-averaged Navier–Stokes (RANS) simulations using the open-source software package OpenFOAM in combination with a multiple rotating
frame (MRF) approach. Therein, the full rotor geometry is resolved in its
own frame of reference and the flow is calculated around the “frozen rotor”.
The subdomain is connected to the stationary frame of reference by an
arbitrary mesh interface (AMI). A grid independency test was executed
investigating different cell sizes, giving an independent result with a
total number of 3.5

M. Lipian, M. Karczewski and P. Wiklak from the Institute of Turbomachinery at Łódź University of
Technology, Poland, contributed two datasets computed by the
commercial CFD software ANSYS CFX. All simulations were performed to find a
steady state solution of the RANS equations using the

For test cases A, B and C they fully resolved the rotor geometry. Thus,
the solver resolves the actual flow around the rotor and no additional
assumptions needed to be made. These simulations will be denoted as fully
resolved rotor model LUT (FRR) from now on. Two rotating
subdomains are established around the rotors, while the main wind tunnel
domain is stationary. A structural mesh is created with the software ICEM
CFD to discretize the domains. The wind tunnel is discretized by a total
number of 3.0

For the test cases B

Overview of turbine operating conditions downstream turbine positions as well as wake measurement positions for the five different test cases.

S. Evans and J. Ryan from CD-adapco, London, United Kingdom, contributed a full dataset of predictions simulated by improved delayed detached eddy simulations (IDDES). The IDDES Spalart–Allmaras turbulence model is used for turbulence
closure in the boundary layers. Both the meshing and the actual simulation
are carried out with their commercial software package STAR-CCM

Aside from the turbine rotors, the exact geometry of the turbine nacelles,
towers and wind tunnel walls is modeled. The computational domain is
divided into three subdomains. In the main wind tunnel domain, a hexahedral
dominant grid is applied, which is further refined around the turbines and
in the wake region. In the disc-shaped regions around the rotors, an
isotropic polyhedral mesh of even finer resolution is utilized. The boundary
layers around the blade surfaces are resolved down to

The inlet conditions are modeled with the synthetic eddy method, generating
an inflow field of defined turbulence intensity and length scales that
correspond to the values given in the invitational document. For test
case C, a shear flow is defined by a power law at the wind tunnel inlet.
Explicit transient modeling is used to simulate the wind turbine
interactions, while the turbine rotations are modeled as a rigid body
motion. A transient second-order model with a time step of
d

More information about the use of Star-CMM

A. Hallanger and I. Ø. Sand from CMR Instrumentation in Bergen, Norway, provided a dataset based on RANS simulations combined with a BEM approach. For the
calculation of the mean and turbulent flow quantities, their in-house CFD
code called Music was used. The RANS equations are solved with a standard

The rotors are included as sub-models in the CFD code. They are represented
by their reaction forces on the flow field. The blade forces are simulated
by a BEM code, including wake rotation. The blades are divided into 30 blade
elements in radial direction. The BEM code includes the Prandtl tip-loss
correction as well as Glauert's empirical model for highly loaded rotors.
The lift and drag coefficients were calculated from the software XFoil
(Drela, 2013) depending on angle of attack, Reynolds number and relative
turbulence intensity. Therein, the transition amplification numbers
(

Wind tunnel walls were modeled by wall functions. The entire wind tunnel
environment including the two rotors was resolved in a total of 5

In total, five different test cases are provided for simulation in this blind test experiment. An overview of the turbine operating conditions and position as well as the measurement station of the wake measurements is shown in Table 2.

For all five test cases the power coefficients

Furthermore, the horizontal profiles of the mean and turbulent flows are
compared at the predefined wake measurement positions (Table 2). The
upstream turbine is still operated at

Therefore, the isotropic normal stress approximation (Eq. 8) is used to
determine the turbulent kinetic energy in each measurement point:

For the LDA measurements the stream-wise and cross-wise flow
components

The computed values of mean velocity as well as turbulent kinetic energy
from HWA and LDA measurements compare very well. In regions of increased
rotation, as in the wake center, the HWA consistently predicts slightly lower mean
velocity values. Here, the influence of binormal cooling velocity

The predictions of the power coefficients

The predictions of the mean and turbulent wake flow

A perfect model prediction would result in a FB and NMSE of zero and MG, VG
and

FB and MG are measures of the systematic error, while FB is measured on a
linear scale and MG is based on a logarithmic scale. Note that it still
might be possible to get a perfect correlation using FB and MG even though the
single points are far off at the specific measurement locations. Conversely, NMSE and VG represent the scatter in the correlation of measured
and predicted data and include both systematic and random errors (Chang and
Hanna, 2004). Finally, the widely used correlation coefficient

The comparisons of the predictions and experimental results are analyzed for
the different inflow conditions. In Sect. 3.1, power, thrust and wake
predictions for test case A (low-turbulence inflow) are presented.
Thereafter, all the test cases for high-turbulence inflow conditions for all
three separation distances (test cases B

Experimental results for power and thrust are indicated by filled black circles for the upstream turbine and empty circles for the downstream turbine. The measurements of the wake profiles using HWA are marked with filled black circles, while flow measurements using LDA are indicated by filled grey circles. The different contributions of numerical simulations are assigned one consistent symbol and color for power, thrust and wake flow predictions.

Power coefficient

Numerical values of power coefficient

The power and thrust predictions for test case A (low-turbulence inflow,
TI

The experimentally measured power coefficient of the upstream turbine has
its maximum

The predictions of the power coefficient of the upstream turbine T1 at its
design operating point

The scatter in

The predictions of the thrust coefficient for turbines T1 and T2 give a
similar picture, as shown in Fig. 5b. Even though the upstream turbine
thrust is slightly underpredicted by most simulations, the scatter is
significantly smaller than in earlier blind tests. The

For the low inlet turbulence test case A, predictions of the wake flow at

Normalized mean velocity

Statistical performance measures FB, NMSE, MG, VG and

As already observed in a very similar test case in blind test 1 (Krogstad
and Eriksen, 2013), the mean velocity profile at

The normalized turbulent kinetic energy profiles are compared in Fig. 6b.
The experimental profile shows two distinct peaks in the shear layer
generated by the tip vortices around

Power coefficient

Numerical values of power coefficient

Normalized mean velocity

Statistical performance measures FB, NMSE, MG, VG and

A second set of power and thrust predictions is compared for inflow
conditions of higher turbulence. A turbulence grid installed at the wind
tunnel inlet generates a uniform wind field with a turbulence intensity
of TI

Comparing the upstream turbine power curve for high background turbulence
(test cases B

The predictions of

Increasing the turbine separation distance to

With a further increase in turbine separation distance to

For the high background turbulence test case B, the participants were asked
to predict the mean and turbulent wake characteristics at three downstream
distances

The wake characteristics of the flow

The fact that all predictions approximated the level of mean velocity
deficit fairly well is also reflected in the statistical performance
measures as presented in Table 6 (upper left section). FB

Very good predictions of the distribution of the turbulent kinetic energy
are presented by CD-adapco as well as UU-DTU. Both simulations predict the
magnitude and location of the two peaks around

Moving downstream to

The turbulence profiles for

A challenging test case is shown for the wake measured at downstream
position

Power coefficient

Analyzing the turbulence profile as shown in Fig. 8f, the tip vortex peaks
decay to about 50 % of the magnitude measured at 5.18

Numerical values of power coefficient

Normalized mean velocity

Conversely, LUT's ACL model underpredicts the turbulence
considerably. Higher deviations in MG

For the last test case the complexity of the inflow conditions is increased.
The inflow to the test section is no longer spatially uniform. Another
custom-made grid with vertically increasing distance between the horizontal
bars is placed at the test section inlet, generating a shear flow that can be
approximated by the power law exponent

Comparing the upstream turbine power curve of test case C (Fig. 9a) to
the upstream turbine power curve of uniform inflow test case B (Fig. 7c),
a very similar curve shape is observed. Taking a closer look, however, a
slightly lower maximum power coefficient is measured in case C and a
marginally earlier run-away point is found at

Statistical performance measures FB, NMSE, MG, VG and

The predictions of

Analyzing the performance results of the downstream turbine at

One single wake profile behind the upstream turbine is compared for test
case C, in which the turbine is exposed to highly turbulent shear flow at the
test section inlet. The mean and turbulent wake characteristics at

The mean velocity profile (Fig. 10a) has a very similar shape to the wake
behind the same turbine exposed to uniform inflow of the same turbulence
intensity (Fig. 8a). The mean velocity profile for shear inflow is also
characterized by two distinct minima and a smooth transition from the wake
to the free stream. Taking a closer look, the wake in case C is slightly
skewed compared to the one measured in test case B. Especially the minimum
velocity peak at

Four different predictions are compared since Vrije did not simulate test case C. As observed for the earlier test cases, UU-DTU's LES simulation predicts
the mean wake shape very accurately. The levels of the two minima are
matched very closely, which is also reflected in a high correlation
coefficient of

Analyzing the turbulent kinetic energy profiles for test case C (Fig. 10b), obvious similarities to those of test case B (Fig. 8b) are
observed. UU-DTU's simulations match the experimental results very
accurately in the center and the tip region, whereas the turbulence level in
the free stream is slightly too high. A similar correlation coefficient

Five different research groups predicted the performance and wake flow between two in-line model wind turbines with a number of different simulation methods. The methods cover different approaches, ranging from commercial software to in-house developed codes. The effects of three different inflow conditions, low-turbulence uniform inflow (test case A), high-turbulence uniform inflow (test case B) and high-turbulence nonuniform shear inflow (test case C) are investigated.

The performance of the upstream turbine (

Comparing wake profiles behind the upstream turbine, it can be concluded that
both CD-adapco's IDDES computations and UU-DTU's LES simulation consistently
deliver very accurate predictions of the experimentally measured mean and
turbulent characteristics for all inflow conditions and separation
distances. CD-adapco and UU-DTU clearly score highest in the statistical
correlation coefficients for all the test cases. It seems that CD-adapco's
IDDES simulations have a marginally better resolution of flow details, as
reflected in very accurate predictions of the shape of the mean velocity and
turbulence intensity profiles. This could be due to a better resolution of
the small scales in the boundary layers of the rotor, hub and tower
geometry, in which the IDDES technique takes advantage of a finer grid
resolution in a RANS model. The very precise predictions of the wake shape
are also confirmed in a marginally higher score of the correlation
coefficients

The mean wake profiles are well predicted by the fully resolved

CMR's wake predictions based on the

The discussion in the workshop disclosed that the quality of the wake predictions is dependent not only on the turbulence model, but rather a complex combination of user-dependent factors. These could be different methods of meshing, choice of turbulence parameters or force coefficients for rotor modeling, for example. Nevertheless, this blind test also confirms that it is possible to make very accurate performance and wake flow predictions given that the model and input parameters are chosen correctly.

The data presented are available from the authors on request.

The authors declare that they have no conflict of interest.

The authors would like to thank the support of NOWITECH for the organization of the workshop. Edited by: J. Peinke Reviewed by: three anonymous referees