Introduction
In order to improve wind turbines, new strategies and concepts have been
developed over the last couple of years. Prior to their application on real
wind turbines, they have to be analyzed in detail and the underlying
processes have to be completely understood. In many cases, investigations
take place on model wind turbines, which is less expensive than building a
full size prototype. Moreover, in wind tunnel tests, reproducible inflow
conditions can be created.
, for example, investigated the interaction among
the wakes of turbines under yawed conditions. They used particle image
velocimetry (PIV) for flow physics studies on this complex interaction
phenomenon. In subsequent investigations, see , they
additionally used hot-wire anemometry to analyze the flow upstream of the
turbine, as well as in the near-wake and far-wake regions.
used hot-wire anemometry to characterize, amongst
others, the distribution of mean velocity and turbulence intensity in the
cross section of a wind tunnel at different locations downwind of a wind
turbine. examined the wake of a model wind
turbine under uniform inflow and under the influence of free-stream
turbulence in terms of 3-D effects. For these investigations, as well as for
the investigations of a model wind turbine under yaw misalignment,
two-component hot-wires were used to measure the velocity fields.
Even a micro wind farm can be installed in a wind tunnel to investigate the
unsteady loading and power output variability; see . used the same experimental
setup of the micro wind farm to investigate the power output for a variety of
yaw configurations.
Moreover, wind tunnel measurements can be used to validate and further
develop numerical codes. In the MEXICO project
, comprehensive measurements of a three-bladed rotor
model of 4.5 m diameter were conducted. The experimental data
were used, for example, to validate numerical methods.
, for instance, used the PIV data, together with
the pressure distribution, to validate their computational fluid dynamics
(CFD) simulations. Blind tests, for example of an unsteady aerodynamics
experiment as performed in the NASA Ames wind tunnel , can be
used to improve the development of wind turbine aerodynamics codes and the
provided data can also be used for their validation.
If the model wind turbine is investigated in a closed test section, the wind
tunnel walls can influence the results. The extent of this influence depends
on the blockage ratio, which is defined as the rotor-swept area divided by
the wind tunnel cross section. , as well as
, investigated model wind turbines in wind tunnels with a
blockage ratio of approximately 10 % and made no blockage correction.
quantitatively investigated the effects of tunnel
blockage on the power coefficient of a horizontal axis wind turbine in a wind
tunnel through experiments. They confirmed the results of
and , as they found, that
the blockage correction is less than 5 % for a blockage ratio of 10 %.
, who experimentally investigated the wakes of
wind turbines in a wind tunnel, also showed that for a blockage ratio smaller
than 10 %, no blockage effect should be experienced and the wind tunnel
walls can be neglected. performed large-eddy
simulations in order to investigate the blockage effects on the
wake and power characteristics of a horizontal-axis wind turbine. Thereby,
the turbine was modeled with the actuator line technique. They found that
for the operation of the wind turbine close to or above the optimal tip speed
ratio, even blockage ratios which are larger than 5 % will have a
substantial impact on the turbine performance.
performed unsteady Reynolds-averaged
Navier–Stokes (URANS) simulations of a model wind turbine in a
cylindrically shaped wind tunnel. To save computational time, the rotational
symmetry of the turbine was exploited and only one-third of the rotor was
simulated. In such a 120∘ model, periodic boundary conditions are
used, solely one blade is taken into account and the tower is neglected. In
this wind tunnel, the blockage ratio is > 50 %. A strong influence of the
wind tunnel walls was experienced, leading to a more than 60 % increase in
the driving forces and 25 % in the thrust on average. The full model of the
same turbine in the real wind tunnel (blockage ratio 40 %) was simulated by
. Thereby, an increase of 25 % in thrust and
50 % in power was experienced.
But until now, the performance of a model wind turbine at such a high
blockage ratio has not been verified with experimental data.
Thus, the provision of experimental data for the validation of the numerical
approaches is one of the three objectives of the present study. The second is
the estimation of the influence of the wind tunnel walls. It will be
evaluated by comparing CFD simulations with and without wind tunnel
walls to experimental data. The third deals with the comparison of codes with
different degrees of fidelity.
In the present paper, the same model wind turbine and wind tunnel as used by
will be investigated experimentally and
numerically. The studied Berlin Research Turbine (BeRT), see
, was designed and built by TU Berlin and
Smart Blade GmbH with contribution from TU Darmstadt in the
aerodynamic blade design. The measurements are conducted in a circuit wind
tunnel and the simulations are performed with two methods with different
degrees of complexity. A lifting-line free vortex wake (LLFVW) code
(QBlade) simulates the turbine under free-stream conditions. In the
numerical setup of the CFD code FLOWer, the wind tunnel walls
and the nozzle are taken into account, but also a case with far field, in
which
the walls are neglected and the boundaries of the setup are far off, is
simulated in order to estimate the influence of the wind tunnel walls and to
enable a better comparison to the QBlade results.
One baseline case and two different yaw-misalignment cases of the turbine are
investigated in this study. All simulations are conducted with uniform
inflow. At cutting planes upstream and downstream of the turbine, velocities
are compared between the experiment and FLOWer. The on-blade velocities
and angles of attack (AoAs), as seen by defined blade sections, are compared
among the experiment, QBlade and FLOWer. As the determination of
the AoA in CFD is complex, two different methods are used in
CFD. Moreover, the bending moments at the blade root are compared
between QBlade and FLOWer.
The numerical and experimental investigation of the turbine is part of the
DFG PAK 780 project , in which six
partners from five universities work together in the field of wind turbine
load control.
Data acquisition
This section deals with the data acquisition of the velocity planes,
on-blade velocity, AoA and bending moments for
each experiment and simulation. Figure shows the
position of the velocity planes as well as the evaluation surfaces for the
CircAve (LineAve with circles) method for the AoA determination
in FLOWer (see Sect. ) exemplary at
blade 1 and the surfaces used for the reduced axial velocity (RAV) method of AoA
determination in FLOWer (see Sect. ).
Position of the velocity planes for the RAV method
(yellow), surface for the determination of the AoA with the CircAve
method (blue) and velocity planes (red).
Generation of the velocity planes
In the experiment, the three red dots in Fig. a at
x=-0.43 d, x=0.5 d and x=1.05 d indicate where hot-wire measurements are
conducted. A semiautomatic traverse with four cross-wire probes with a
measurement frequency of fs=25kHz and a cutoff frequency of
fcut=10kHz is used. Each of the 608 measurement positions, Fig. b,
in each cross section is measured for
Ts=16s. This time is assumed to be long enough for good
statistics for the current setting as the measured integral timescale is
≤0.023s, which is considerably smaller than the acquisition time
of 16s. With the inflow velocity of 6.5ms-1 as
convective velocity, an integral length of 0.023s⋅6.5ms-1=0.15m is calculated based on Taylor's hypothesis.
Offset correction among the probes was realized by repeating 19
measurement points along a vertical line with all four probes. For each
measurement position, the mean value of all four measurements was calculated
and used as reference. Subsequently, the offset of each probe was calculated.
This offset was averaged over all measurement points. Thereby, the offset for
each probe was calculated, which was then applied to all measurements in
post-processing. The calibration of the probes was performed with the help of a
nearby pitot probe at different wind tunnel velocities.
The error of the hot-wire measurements is the sum of the calibration setup
error (pitot tube, pressure sensor) and the hot-wire anemometry hardware. The
latter was calculated by measuring multiple points in each test case with all
probes and the largest deviation is defined as the error. In the present case
it amounts to 3.3%, which corresponds to 0.33ms-1 in reference to
the maximum calibrated velocity. This is in good agreement with error
estimations given in literature; see . The total error,
including calibration setup, is calculated to be 4.4%, corresponding to
0.44ms-1.
Only the simulation including wind tunnel walls has been taken into account
for the comparison of the velocity planes. In this setup, at each point of
the numerical grid, data were extracted for the planes and averaged over five
revolutions. In order to evaluate the differences between measurement and
simulation, the results of the simulation are interpolated to a grid with the
same grid points as the measurement points and the results are subtracted.
Extraction of the on-blade velocity and the angle of attack
The AoA is the angle between the velocity, as seen by the
blade (on-blade velocity), and the airfoil chord. Generally, deriving an
AoA in rotating domain is somewhat difficult, as the AoA is a
two-dimensional value. Moreover, the blade deflects the streamtraces due to
its induction and therefore changes the value of the AoA.
In the experiment the AoA and the on-blade velocity are measured by
three-hole probes located at 65 and 85%R. The derivation of the
sectionwise values, referenced to the quarter-chord point of each section,
is detailed by and will be explained here
shortly. Generally, this measurement method is advantageous, as no static
tunnel reference pressure is needed and short tubing, as the pressure sensors
are located in the blade, mitigates possible delay effects. The three-hole
probes measure the αprobe and Urel,probe in reference to the
probe position upstream of the wing. These values are derived by calibration
of the pressure differences among tubes to the flow angle and velocity.
However, when mounted on the wing, the results are affected by the induction
of the blade and therefore need to be translated into the sectional AoA α and the relative velocity Urel. In this project a
procedure based on two-dimensional flow assumption on the wing, Fig. , was employed.
Schematic and flow chart of derivation of the sectionwise AoA .
Herein, αprobe is first rotated into the local coordinate system,
which is based on the local chord, to derive αprobe,section.
Subsequently, a look-up table is used, which was derived with viscous
XFOIL calculations. This table correlates the
measurement at the probes' head upstream of the wing to the actual local
section AoA α. Thereby, the induction effect is accounted
for and α and Urel are found. The analysis showed that the
dependency of the local flow angle at the probe to the actual AoA is almost a
first-order function in the linear region of the lift polar (the AoA range
in which the lift has a nearly constant slope). The approximated equation (Eq. )
gives information about the order of conversion for this
2-D approach.
α=0.58∘⋅αprobe-0.64∘
The data set was created by analyzing polars from α=-30 to
30∘ in steps of 0.5∘. Steps in between are interpolated. This
procedure requires two-dimensional flow over the blade, which is assumed to
be appropriate in this case, in comparison to quantitative tuft flow analysis
, which indicated few three-dimensional effects
on the surface flow.
In order to estimate the measurement error of the three-hole probes, data
sets from calibrations of the probe alone and of measurements of the probe
installed in a 2-D-wing setup were analyzed. The data sets include variation
in AoA from -30 to 30∘ and the variation in the free-stream
velocity. From this analysis, which also includes the error of the induction
correction and sensor uncertainties, the maximal absolute error for AoA was
estimated to be 0.8∘ (considering only the attached flow regime) and
for the on-blade velocity it was estimated to be 0.4ms-1.
In QBlade, the AoAs are evaluated at the quarter chord
position of the airfoils at the lifting line (the bound vorticity) of the
rotor blades. The AoA is calculated from the part of the absolute
velocity vector that lies inside the respective airfoils cross-sectional
plane – which corresponds to the on-blade velocity. The absolute velocity
vector itself is a superposition of the inflow, relative, wake-induced and
self-induced velocity vectors.
Different methods to derive the effective sectional AoA from 3-D CFD-predicted flow fields are compared and evaluated by
. Details of the methods are described in that
paper. The two methods, which are most suitable for the present case,
are used for the AoA extraction shown in this paper. The RAV method uses two planes, one
upstream and one downstream of the rotor (see Fig. ). In
these planes, the average velocities are calculated and afterwards the
velocity components are used to determine the velocity in the rotor plane
without the induction of the blade. The method is based on the method of
, who determined airfoil characteristics from 3-D
CFD rotor computations. It was successfully applied by
to investigate unsteady 3-D effects on trailing
edge flaps, and by for CFD analysis of a
two-bladed multi-megawatt turbine. In the line averaging method (LineAve
or CircAve), the AoA is determined by averaging the velocity over a
closed line around each blade cut (see Fig. ). For both
approaches, the results are averaged over five revolutions.
Determination of the bending moments
In the present paper, the flapwise (out of plane) moment (My) and the
edgewise (in plane) moment (Mx) are investigated.
Due to problems with the full-bridge strain-gauge setup in the experiment,
strong fluctuations are visible in the raw data and heavy filtering was
necessary. Therefore, the bending moments cannot yet be considered a valid
basis for quantitative comparisons and code validation purposes.
In the LLFVW method of QBlade the blade bending moments are
evaluated by summing up the elemental blade forces, obtained from an
integration of the normal and tangential forces along the blade span that are
obtained via the stored airfoil coefficients.
In the CFD simulation, the bending moments in the blade root result
from the pressure and friction on the blade surface. For each surface cell
the forces are computed and multiplied with the corresponding radius. Then
they are averaged over five revolutions.
Results and discussion
Comparison of the velocity planes
The velocity planes, which are taken into account in the present study, are
placed 0.43 d upstream and 0.5 d downstream of the rotor plane (see Fig. ).
The plane 1.05 d downstream of the rotor plane (see
Fig. ) is neglected in the present study, as the evaluation
would not have brought further benefit for the paper. Moreover, at this
location, the influence of the nozzle is already present, which influences
the wake development on top of the wind tunnel walls.
Figure a shows the velocity in x direction for
the measurement and Fig. b for the FLOWer wind tunnel
simulation 0.43 d upstream of the rotor plane. The measuring points are
shown as black dots. The dimensions of the wind tunnel, as well as the model
wind turbine, are illustrated by dashed lines. Moreover, an isoline with the
undisturbed inflow velocity of 6.5ms-1 is shown. The view
direction in this picture, and in all following figures of the velocity
planes, is from downstream to upstream.
: Hot-wire measurements (a) and simulated velocity
plane (b)
of the x velocity 0.43 d upstream of the rotor plane. The dashed lines
illustrate the wind tunnel and the turbine. Isolines show the undisturbed
inflow velocity of 6.5ms-1. The dots in (a) show the
discrete measuring points.
The turbine blockage effect can be observed in both figures. However, the
velocity distribution in the simulation is smoother and axisymmetric, leading
to a clearly defined blockage, whereas it is more frayed in the experiment.
Due to the location of the settling chamber after a corner, see Fig. ,
the measured x velocity on the left side differs slightly
from the velocity on the right side. Additionally, a difference at the bottom
and upper position is apparent. Due to construction reasons, the mounting
of the aforementioned filter mat (see Sect. )
leaves a small gap at the ceiling of the wind tunnel; a small velocity
overshoot is present at the top of the inflow test section. In the
simulation, a slightly higher velocity can be seen in the corners of the wind
tunnel.
In the experiment, multiple causes of possible measurement errors, such as
temperature compensation or induction of the traversing system, are analyzed
and ruled out. Therefore, the horizontal inequalities seem to result from the
design of the wind tunnel. More information about the hot-wire measurements
and possible reasons for the inequality of the flow field can be found in
.
Table gives an overview of some mean parameters
characterizing the velocity plane 0.43 d upstream of the rotor plane. In the
experiment, the averaging was carried out over the measuring time, in the simulation
over five revolutions.
Mean parameters for the velocity plane 0.43 d upstream of the rotor plane.
u‾ (ms-1)
σu‾ (ms-1)
Ti‾global(uv) (%)
Measurement
6.42
8.50×10-2
1.20
FLOWer
6.47
–
–
The mean velocities in the streamwise direction are slightly smaller than the
desired velocity, both for measurement and simulation. However, as the
differences are <0.5% in the simulation and ≈1% in the
measurement, the reference velocity can still be considered to be
6.5ms-1 As uniform inflow was used in the present simulation, the
standard deviation and turbulence intensity are negligible. The turbulence
intensity of the measurement corresponds to the value of the wind tunnel,
which was already mentioned in Sect. . The
unsteady inflow in the experiment and the uniform inflow in the simulation
lead to a discrepancy in the setups. The influence of the turbulence on the
results will be discussed later in this document and reviewed in future
investigations.
In Fig. , the relative difference between
simulation and measurement with regard to the mean inflow velocity of
6.5ms-1 is shown.
Relative velocity difference between measurement and simulation with
regard to the undisturbed reference inflow velocity of 6.5ms-1,
0.43 d upstream of the rotor plane. The dashed lines illustrate the wind
tunnel and the turbine. Isolines show 0% deviation. The dots show the
discrete evaluation points.
The differences between both velocity planes are small as the average
deviation amounts to ≈3%. Except for a small area at the bottom of the
wind tunnel (around z=0.5m and between -1m<y<0m), the difference is lower than ±10% of the desired inflow
velocity, which corresponds to ±0.65ms-1.
Figure shows the velocity in x direction 0.5 d
downstream of the rotor plane, for the measurement (top) and for the
simulation (bottom). Again, the measuring points are indicated by black dots,
the dimensions of the wind tunnel and the model wind turbine by dashed lines.
An isoline with the mean velocity of 6.5ms-1 is shown, too.
Hot-wire measurements (a) and simulated velocity plane (b) of
the x velocity 0.5 d downstream of the rotor plane. The dashed lines
illustrate the wind tunnel and the turbine. Isolines show the mean inflow
velocity of 6.5ms-1. The dots in (a) show the
discrete measuring points.
Some aspects, as already seen upstream of the rotor
(Fig. ),
are apparent downstream of the rotor, too, for
example the higher velocity over the ceiling in the measurement or the
smoother, axisymmetric streamwise velocity in the simulation. In Fig. 10a, b the wake of the rotor, indicated by lower velocity, can be
seen clearly. Around the rotor, as a result of limited space due to the wind
tunnel walls, higher velocities are achieved. Again, in the experiment, the
velocity at the upper part of the wind tunnel is slightly higher than at the
bottom.
This missing turbulence in the simulated wind tunnel is the reason why the
border of the rotor wake is almost a perfect circle in the lower picture,
whereas it is more smeared in the measurement. The decay of the tip vortices
has not yet started so shortly behind the rotor plane. As the simulation has
a finer resolution, the velocity distribution is smoother there. In the
simulation, there is a stronger velocity deficit in the wake of the nacelle.
This can have several reasons. In the simulation, the missing inflow
turbulence might have a small effect on the stability of the wake, but it is
certainly not the main reason for the deviation; see
. In the experiment, the boundary layer of the
nacelle is not tripped, whereas a fully turbulent approach is used in the
simulation. These differences concerning the boundary layer of the nacelle
might lead to a different recovery of the wake of the nacelle. Due to the
flow separation on the nacelle, the flow in the wake of the nacelle is highly
unsteady and the main flow direction is not clearly defined (angles larger
than ±60∘ occur in the simulation), whereby proper working
conditions of the x-wire probe are no longer guaranteed. Therefore, the
measured x component of the velocity is influenced by the y and z components,
which could also lead to deviations between measurement and simulation.
An overview of some mean parameters characterizing the velocity plane 0.5 d
downstream of the rotor plane are given in Table .
Mean parameters for the velocity plane 0.5 d downstream of the rotor plane.
u‾ (ms-1)
σu‾ (ms-1)
Ti‾global(uv) (%)
Measurement
6.53
6.76×10-1
7.01
FLOWer
6.48
3.17×10-1
3.71
Again, the mean velocity almost corresponds to the desired reference
velocity, as the differences between the actual velocity and
6.5ms-1 are <0.5% for both measurement and simulation. Due to
the closed wind tunnel and the mass continuity, bigger differences would not
have been physical. As the tip and root vortices, as well as the separation
behind the nacelle, lead to velocity fluctuations, the standard deviation, as
well as the turbulence intensity, increase compared to the plane upstream
from
the rotor; see Table . Through the superposition of the
vortices created by the turbine and the inflow turbulence, the values for the
measurement are still larger. As the present wind tunnel is a circuit wind
tunnel, effects like pumping might occur. And due to the long measurement
time of the hot-wire probes, these fluctuations might also be included in the
values shown in Table .
Figure shows the relative difference between
simulation and measurement with regard to the mean inflow velocity of
6.5ms-1.
Relative velocity difference between measurement and simulation with
regard to the undisturbed reference inflow velocity of 6.5ms-1,
0.5 d downstream of the rotor plane. The dashed lines illustrate the wind
tunnel and the turbine. Isolines show 10% deviation. The dots show the
discrete evaluation points.
It can be seen that in the wake of the nacelle and in the area of the tip
vortices, the differences between simulation and measurement are higher than
10%. In the remaining part, the difference is smaller. The mean deviation
amounts to ≈7%, which is considerably higher than the value for the
plane upstream of the turbine. The reason for the high value is primarily the
area in the wake of the nacelle, where differences >50% occur. If a
circular area with a radius r<0.56m and its origin at the center of
the rotor is neglected in the averaging, the mean deviation reduces to <6%
as the mean deviation in this area itself amounts to about 31%. Thereby it
has to be kept in mind that due to the large flow angles in the wake of the
nacelle, the measured values in this area have to be treated with caution.
All things considered, the accordance between experiment and simulation is
acceptable, as the differences are, except for some parts in the outer region
of the rotor and in the wake of the nacelle, smaller than
±0.65ms-1.
Analysis of the on-blade velocity
Hereinafter, the on-blade velocity, meaning the velocity seen by the blade
section at a distinct radial position, for CaseBASE for the experiment,
QBlade and FLOWer (both methods RAV and CircAve)
are displayed at two different rotor locations (65 and 85%R) over the
azimuth (Fig. ). A radius of 0%R corresponds to the
rotor center, whereas an azimuth of 0∘ corresponds to the top
position of the first blade.
On-blade velocity distribution over the azimuth for CaseBASE for the experiment,
QBlade and FLOWer (RAV and CircAve for wind tunnel and far field each) at 65%R (a) and
85%R (b).
At 65%R, the simulations overestimate the velocity; at 85%R there is a
better accordance between the simulation results and the experiment. The
difference caused by the different inflow turbulence is even less pronounced
at the on-blade velocity compared to the velocity planes, as the rotational
velocity has a much higher influence than the inflow velocity. Therefore, the
fluctuations in the measurements are not so distinct and the differences
between measurement and simulation caused by the inflow turbulence are small.
For their cases with and without free-stream turbulence,
also experienced only small differences in the
drag coefficient, which depends on the AoA and consequently also
on the on-blade velocity. The higher fluctuations in the experiment at the
outer radial position might be a result of a vibration of the mounting of the
probe. The averaged standard deviation for the measured velocity amounts to
σon-blade(65%R)=0.11ms-1 and
σon-blade(85%R)=0.08ms-1.
In order to better assess the quantitative differences among the curves,
Table gives an overview of the relative differences
between the experiment and the different simulation results of the averaged
on-blade velocity (Δv‾=vSim‾-vExp‾) for CaseBASE at both probe
positions.
The reference velocity in each case is the undisturbed velocity at the probe
position, which was calculated with
vRef=vinflow2+(ω⋅R)2
and amounts to vRef(65%R)=19.49ms-1 and
vRef(85%R)=24.90ms-1.
Relative differences between the experiment and the different
simulation results of the averaged on-blade velocity with respect to the
undisturbed velocity at the probe positions for CaseBASE.
Δv‾ (%)
65%R
85%R
QBlade
2.05
0.25
FLOWer-RAV
3.90
1.68
FLOWer-CircAve
3.72
1.44
FLOWerFF-RAV
2.31
0.68
FLOWerFF-CircAve
2.10
0.43
For both radial positions, all simulations match fairly well to each other,
as the differences from the experiment are relatively similar. However, all
simulations overestimate the experimental results. For the FLOWer
simulations, both methods (RAV and CircAve) show almost the
same results (Δv‾FLOWer-RAV and Δv‾FLOWer-CircAve≈4% at 65%R and Δv‾FLOWer-RAV and Δv‾FLOWer-CircAve<2%
at 85%R), whereby the CircAve method seems to fit better to the
experimental results. In the outer part of the blade, where the probes are
located, the on-blade velocity is dominated by the tangential velocity.
Consequently, both FLOWer setups (wind tunnel and far field), show
almost the same results, too. But due to the wind tunnel walls, the inflow
velocity in the rotor plane is slightly higher than in the far field case,
which can be seen in the marginally higher curves for the wind tunnel case.
With increasing radius, the difference between the wind tunnel and the far
field case decreases, as the rotational part of the velocity becomes more and
more dominant. The QBlade results are closest to the measured data,
which is surprising, as the wind tunnel walls are not taken into account in
the LLFVW simulations. Due to the lack of walls, they have a
better accordance with the FLOWer far field results than with the ones
including the walls. The influence of the tower blockage around an azimuth of
180∘ can be seen at both radial positions as a small increase before
the tower passage and a small drop afterwards. The increase in the inflow
velocity is due to the displacement effect of the tower. Directly upstream of
the tower, the velocity is reduced until it has recovered shortly afterwards.
Except for this drop, the velocity is almost constant over the whole
revolution.
Figure shows the velocity over the azimuth under
yaw = -15∘. As the wind tunnel walls should not be neglected in the
present setup, a far field case under yawed conditions for FLOWer was
not simulated.
On-blade velocity distribution over the azimuth for CaseYAW15 for the experiment,
QBlade and FLOWer (RAV and CircAve) at 65%R (a) and 85%R (b).
Under 15∘ yaw misalignment, the averaged standard deviation for the
measured velocity is the same as for CaseBASE
(σon-blade(65%R)=0.11ms-1 and
σon-blade(85%R)=0.08ms-1). Table
gives an overview of the relative differences
between the experiment and the different simulation results of the averaged
on-blade velocity for CaseYAW15 at both probe positions.
Relative differences between the experiment and the different simulation
results of the averaged on-blade velocity with respect to the undisturbed velocity at the probe positions for CaseYAW15.
Δv‾ (%)
65%R
85%R
QBlade
0.96
-0.54
FLOWer-RAV
3.04
1.05
FLOWer-CircAve
2.87
0.82
At 65%R, the experimental and QBlade results are almost identical
(Δv‾QBlade≈1%), whereas FLOWer predicts a
slightly higher velocity (≈0.5ms-1, which corresponds to
Δv‾FLOWer≈3%). At 85%R, there is still a
small offset between QBlade and FLOWer, but the measurement
lies between the two curves, which can also be seen at the different signs of
the differences in Table . Moreover, as already seen
for the case with no yaw misalignment, the differences are smaller further
outboard. In total, the differences between experiment and simulations are
smaller than under straight inflow.
The influence of the tower is covered by the influence of the yaw
misalignment, which leads to stronger variations over one revolution. In the
upper part of the rotor (azimuth = 270–90∘), the blade
advances, while it retreats in the lower part
(azimuth = 90–270∘). This leads to a 1p variation in
inflow velocity as seen by the blade. Further information and detailed
discussions about effects occurring under yaw misalignment, like the 1p
variation, are summarized by .
In Fig. , where the velocity over the azimuth under
yaw = -30∘ is plotted, the influence of the yaw misalignment is even
more pronounced.
On-blade velocity distribution over the azimuth for CaseYAW30 for the experiment,
QBlade and FLOWer (RAV and CircAve) at 65%R (a) and 85%R (b).
Again, the averaged standard deviation for the measured velocity amounts to
σon-blade(65%R)=0.11ms-1 and
σon-blade(85%R)=0.08ms-1. In Table ,
the relative differences between experiment and the
different simulation results of the averaged on-blade velocity for
CaseYAW30 at both probe positions are displayed.
Relative differences between the experiment and the different
simulation results of the averaged on-blade velocity with respect to the undisturbed velocity at the probe positions for CaseYAW30.
Δv‾ (%)
65%R
85%R
QBlade
-0.79
-1.65
FLOWer-RAV
1.41
0.11
FLOWer-CircAve
1.30
-0.1
Almost the same characteristics as already mentioned with regard to Fig.
can be found for -30∘ yaw misalignment. However,
at 65%R, the FLOWer results have a better agreement with the
experiment in the upper part of the rotor (270 to 90∘
azimuth) than in the lower part (90 to 270∘ azimuth). At
85%R the FLOWer curves and the measured curve correspond well
(|Δv‾FLOWer|≤0.11%), whereas the QBlade
results have a bigger deviation from the experimental results. Overall, the
differences between the simulated curves and the measured curves decrease
again with increasing yaw misalignment.
Evaluation of the angle of attack
As for the on-blade velocity, in the following, the AoA for CaseBASE for the
experiment, QBlade and FLOWer (both methods RAV and
CircAve) are displayed at two different rotor locations (65 and
85 %) over the azimuth (Fig. ).
AoA distribution over the azimuth for CaseBASE for the experiment, QBlade and
FLOWer (RAV and CircAve for wind tunnel and far field each) at 65%R (a) and 85%R (b).
The tower blockage effect can be clearly seen at azimuth = 180∘, where
the AoA has a drop of approximately 1∘. The influence of the tower
is very distinct, due to its relative large diameter, compared to the other
components of the turbine. For both, QBlade and FLOWer, the
curve is almost constant before and after this drop. The dip in the
experiment at an azimuth of approximately 90∘ is a result of the
traverse, which was located in the test section upstream of the rotor.
Table gives an overview of the differences between
the
experiment and the different simulation results of the averaged AoA (Δα‾=αSim‾-αExp‾) for CaseBASE at both
probe positions in order to quantify them. In contrast to the on-blade
velocity, no relative values were calculated.
Differences between the experiment and the different simulation results of the angle of attack for CaseBASE.
Δα‾ (∘)
65%R
85%R
QBlade
-2.48
-2.13
FLOWer-RAV
-0.23
0.03
FLOWer-CircAve
-0.08
-0.03
FLOWerFF-RAV
-2.48
-2.00
FLOWerFF-CircAve
-2.33
-1.95
There is a good accordance between the experiment and the FLOWer
results despite the fact that the simulated curves lie outside of the
measured standard deviation whose average is however small
(σα(65%R)=0.10∘ and
σα(85%R)=0.14∘). Even so, they are within the range of
the maximum absolute error of 0.8∘; compare Sect. . The larger value for the more outboard region
mirrors the effect of the vibrating mounting of the probe. Both AoA
evaluation methods for the FLOWer solution show almost the same
distribution, especially at 85% (|Δα‾FLOWer|≤0.23∘ at 65%R and |Δα‾FLOWer|≤0.03∘ at 85%R). Reasons for the differences can be attributed to
the different approach of the methods (RAV is averaging over time and
CircAve has a local approach; see ). At
65%, the level of the AoA is approximately 0.5∘ lower than
further outboard for the experiment, QBlade and FLOWer.
An offset of >2∘ between the simulation results of QBlade
and FLOWer (including wind tunnel walls) is present for both radial
positions. This is a result of the neglect of the wind tunnel walls in the
QBlade simulation. As the walls impede the expansion of the wake, the
velocity in the rotor plane and consequently the AoA are higher for the
case including wind tunnel. A comparison between the QBlade results
and the FLOWer results under far field conditions verifies this
assumption, as both the distributions and the offsets to the measured
values, see Table , are almost similar. More
information about this phenomenon and the underlying reasons can be found in
and . The small kinks at
≈90 and ≈270∘ azimuth in the QBlade
results are a result of the usage of the tower model. This model has to be
switched on at a certain blade position. In the present simulations this is
carried out as soon as the blade position is located below the nacelle, leading to a
discontinuity, which is reduced through interpolation. However, as the tower
has a relatively large diameter, the kink cannot be completely prevented.
A comparison of the AoA distribution calculated by QBlade and
FLOWer over the normalized radius at an azimuth = 0∘ for the wind
tunnel and far field cases is shown in Fig. .
AoA distribution over the normalized blade radius at an azimuth = 0∘
for QBlade and FLOWer (RAV and CircAve for wind tunnel
and far field each). Black lines indicate the evaluation positions of Figs. , and .
Again, the influence of the wind tunnel can be seen in the constant offset
between the two FLOWer cases. As already seen in Fig. and Table , the offset between the
RAV and the CircAve results amounts to ≈0.15∘ at
65%R and decreases to ≈0.06∘ at 85%R for both cases
(far field and wind tunnel). As already mentioned, the differences are a
result of the different approaches of the two methods; see
. Between approximately 40 and 90% of the
radius, there is a good accordance between the QBlade and the
RAV solution of the FLOWer far field case.
Figure shows the AoA over the azimuth under yaw = -15∘.
AoA distribution over the azimuth for CaseYAW15 for the experiment,
QBlade and FLOWer (RAV and CircAve) at 65%R (a) and 85%R (b).
The same characteristics as under yaw = 0∘ can also be seen in Fig.
under yaw = -15∘. Again, the influences of the
tower blockage and the traverse are clearly visible. Unlike in CaseBASE,
the AoA is not constant before and after the drop caused by the tower, due to
the yaw misalignment.
In Table , an overview of the differences between
experiment and the different simulation results of the averaged AoA for CaseYAW15 at both probe positions is given.
Differences between the experiment and the different simulation results of the angle of attack for CaseYAW15.
Δα‾ (∘)
65%R
85%R
QBlade
-2.05
-1.76
FLOWer-RAV
-0.18
0.13
FLOWer-CircAve
0.01
0.07
As in CaseBASE, the FLOWer results show a good agreement with the
measurements at both radial positions (|Δα‾FLOWer|≤0.18∘ at 65%R and |Δα‾FLOWer|≤0.13∘ at 85%R) and the average of the measured deviation is again
small and similar to the values for the CaseBASE
(σα(65%R)=0.10∘ and
σα(85%R)=0.14∘). Again, the differences of the
CFD results including wind tunnel are smaller than the maximal
absolute error of 0.8∘. The two different evaluation methods for
FLOWer show almost the same results, too. The difference between the
two radial positions amounts to approximately 1∘ for all setups. The
offset between QBlade and FLOWer is >1.8∘ but
smaller than for case CaseBASE and can still be attributed to the influence
of the wind tunnel walls. The reduction of the difference between
QBlade and FLOWer is a result of the yaw misalignment. Through
the rotation of the rotor plane out of the inflow plane, the projected plane
becomes smaller, leading to a smaller blockage in the wind tunnel. As the change
of the projected area follows the cosine function, the changes in the
differences are not linear. As already mentioned, a far field case under yaw
misalignment for FLOWer was not simulated. The kinks at
≈90 and ≈270∘ azimuth are still present, but
less pronounced.
In Fig. the AoA distribution over the azimuth for a yaw
misalignment of -30∘ can be seen.
AoA distribution over the azimuth for CaseYAW30 for the experiment, QBlade
and FLOWer (RAV and CircAve) at 65%R (a) and 85%R (b).
The effects of the tower blockage and the traverse are still visible. The
effects caused by the yaw misalignment are more pronounced here.
An overview of the differences between experiment and the different
simulation results of the averaged AoA for CaseYAW30 at both
probe positions is given in Table .
Differences between the experiment and the different simulation results of the angle of attack for CaseYAW30.
Δα‾ (∘)
65%R
85%R
QBlade
-1.32
-1.25
FLOWer-RAV
-0.02
0.11
FLOWer-CircAve
0.23
0.12
At 65%, there is a difference between the measurement and FLOWer
results at the downward-moving blade (azimuth = 0–180∘),
probably due to the traverse placed in the wind tunnel, whereas there is a
good agreement at the upward-moving blade
(azimuth = 180–360∘). The average accordance between the
experiment and the FLOWer simulations is satisfactory, as the
differences are small (|Δα‾FLOWer|≤0.23∘). Further outboard, the curves correspond very well over the
whole revolution (|Δα‾FLOWer|≤0.12∘),
except for the dip at a 90∘ azimuth. The average of the deviation
amounts to σα(65%R)=0.09∘ and
σα(85%R)=0.13∘, which can be considered small. The
offset between QBlade and FLOWer, due to the missing wind
tunnel walls in QBlade, has decreased and amounts now to <1.6∘.
For all three cases (CaseBASE, CaseYAW15 and CaseYAW30) at both radial
positions, despite the constant offset from the QBlade results, the
amplitude and phase of the AoA of the experiment, QBlade and FLOWer
have a good agreement.
Investigation of the bending moments
In the following, the flapwise bending moments (out of plane, My) for one
blade, simulated with QBlade and FLOWer, are compared to each
other for all three cases. Figure shows the curves for CaseBASE
(Fig. a), CaseYAW15 (Fig. b) and CaseYAW30 (Fig. c).
Simulated flapwise bending moment (My) over the azimuth for CaseBASE (a), CaseYAW15 (b)
and CaseYAW30 (c) for QBlade and FLOWer.
As the forces and moments mainly depend on the AoA, the same characteristics
(tower shadow, influence of yaw misalignment, etc.) as in Figs. , and
can be seen in Fig. , as they cascade down from the AoA to the
loads.
In Table , the relative differences among the
simulation results of the flapwise bending moment are displayed.
Relative differences among the different simulation results of the
averaged flapwise bending moment with respect to the FLOWer solution including wind tunnel walls.
ΔMy‾ (%)
QBlade
FLOWerFF
CaseBASE
8.87
19.64
CaseYAW15
7.86
–
CaseYAW30
2.81
–
The difference between the two FLOWer results for the baseline case
(top figure, ≈20%) represents the influence of the wind tunnel
walls. However, this time, the accordance between the QBlade results
and the FLOWer wind tunnel case (<9%) is slightly better than
between the QBlade case and the FLOWer far field case. This
unexpected result might be a result of the choice of the XFOIL polars
used for the present QBlade simulations because although the AoAs are
similar between QBlade and CaseBASEFLOWer-FF (see Fig. and Table ), the bending moments
differ. Comparisons of the radial moment distribution and of the force
coefficient over the azimuth could lead to a better understanding and
assessment of the differences.
The amplitude and phase of the 1p frequency,
caused by the yaw misalignment, show a good accordance between QBlade
and FLOWer for CaseBASE and CaseYAW15. The mean differences under
yaw misalignment decrease with increasing yaw angle (<8% under
15∘ yaw misalignment and <3% under 30∘ yaw
misalignment), showing the same tendency as the AoA (Tables , and
). Except for the constant offset, the fit between
the curves of the QBlade and FLOWer simulations is similar to
the one for the on-blade velocity and the AoA. This time, the
kinks in the curves at ≈90∘ and especially at
≈270∘ are a bit more pronounced. For all three cases,
QBlade predicts, due to the missing wind tunnel walls, smaller values
than FLOWer.
The comparison of the edgewise bending moments (in plane, Mx) can be found
in Fig. .
Edgewise bending moment (Mx) over the azimuth for CaseBASE (a), CaseYAW15 (b)
and CaseYAW30 (c), for QBlade and FLOWer.
The same characteristics of the curves as for the flapwise bending moments
(see Fig. ) can be found in the simulated edgewise bending
moments.
The relative differences among the different simulation results for the
edgewise bending moments are summarized in Table .
Relative differences among the different simulation results of
the averaged edgewise bending moment with respect to the FLOWer solution including wind tunnel walls.
ΔMx‾ (%)
QBlade
FLOWerFF
CaseBASE
20.82
33.37
CaseYAW15
19.04
–
CaseYAW30
10.67
–
The differences between the FLOWer results with and without wind
tunnel walls are larger than for the flapwise bending moment (ΔMx‾≈33% compared to ΔMy‾<20%; see
Table ). This corresponds to the results of
and , who also
experienced a stronger influence of the walls on the power than on the
thrust. The reason for this phenomenon is attributed to the different
sensitivity of the forces to AoA variations. The tangential force, which is
the main driver of the in-plane moment, is more prone to changes in the AoA compared to the normal force. Consequently, small differences in
the AoA lead to larger deviations in FT than in FN. Other than for
My, the QBlade results for Mx are closer to the FLOWer
far field results than to the wind tunnel results. The progression of the
edgewise bending moment is almost similar between QBlade and
FLOWer for all three inflow directions. The mean differences under
15∘ yaw misalignment (≈19%) are slightly smaller than for
CaseBASE (≈21%), but the difference under 30∘ yaw
misalignment is significantly smaller (<11%) than for the other two
cases. Again, the change in the projected area and the blockage in the wind
tunnel can be alluded to as reason for this tendency.
To sum up, the progression
of the curves fit quite good for both moments, except the kinks caused by the
tower shadow model in QBlade. The offset among the results seems to
depend on consideration of the wind tunnel walls and the chosen polar set
in QBlade. The decreasing differences between QBlade and
FLOWer with increasing yaw misalignment are a result of the decreasing
projected rotor plane, which influences the blockage in the wind tunnel.
Summary
Experimental and numerical investigations of a model wind turbine, placed in
a wind tunnel with a high blockage ratio, were presented in the present paper.
Thereby, two codes of different fidelity were used. In the simulations
conducted with the lifting-line free vortex wake code QBlade, the wind
tunnel walls had to be neglected and the turbine was simulated under far
field conditions. Unsteady Reynolds-averaged Navier–Stokes simulations have
been performed with the CFD code FLOWer.
Thereby, a far field case, as well as simulations including the wind tunnel
walls, were investigated. In all simulations, the tower was considered, but
they have been performed under uniform inflow, neglecting the turbulent
inflow in the experiment.
The experiments provided validation data and the comparison between
experiment and the FLOWer wind tunnel case aimed at the validation of
the CFD simulation. Through the comparison between two FLOWer
cases (wind tunnel and far field) the influence of the blockage ratio was
assessed. With the knowledge about the influence of the wind tunnel walls,
the suitability of the LLFVW code to perform preliminary
investigations for future studies with the model wind turbine could be
investigated by a comparison between QBlade and the FLOWer
far field case.
A comparison between the measured flow fields and the velocity planes
extracted from FLOWer simulations including wind tunnel walls was
conducted. Thereby, two different velocity planes were investigated. One is
located 0.43 d upstream of the turbine, one 0.5 d downstream. The velocity
fields upstream of the turbine showed a good agreement in the rotor area, as
the average deviation amounts to about 3% of the inflow velocity. Downstream
of the rotor plane, the differences were more pronounced (mean deviation of
≈7% of the inflow velocity). The areas of the tip vortices and the
wake of the nacelle are most prominent. The differences between the
experimental and numerical results upstream and downstream are caused,
for example, by vertical shear and higher turbulence in the measurements.
Additionally, the differences in the wake of the nacelle and the outer region
of the rotor might be caused by the high flow angles influencing the hot-wire
measurement downstream of the rotor.
At two radial positions (65 and 85%R), the on-blade velocity and the
AoA were measured with three-hole probes and compared to the results obtained
from QBlade and both FLOWer cases. For the investigation of
these parameters, three different yaw cases (yaw = 0, -15
and -30∘) were considered.
The mean deviations of the on-blade velocity between the experiment and each
simulation are <4% at 65% of the radius and <2% at 85% of the
radius.
The AoA calculated with FLOWer including wind tunnel showed a good
agreement with the experimental results, as the maximum mean difference
amounts to 0.23∘. As the QBlade results and the FLOWer
simulation without wind tunnel walls are almost similar, the constant offset
of approximately 1–2∘ between the experiment and the far
field simulations is a result of the neglect of the wind tunnel walls.
Finally, the blade root bending moments are compared between QBlade
and the two FLOWer cases. For the out-of-plane bending moment, the
difference between the two FLOWer cases (far field and wind tunnel)
can be accredited to the influence of the wind tunnel walls. The offset
between the QBlade results and both FLOWer cases cannot only
be attributed to the influence of the wind tunnel walls. As the bending
moments differ between the two far field cases despite the good accordance
concerning the AoA, the chosen set of airfoil polars, which is used in the
QBlade simulations, influences the loads. The accordance between the
calculated amplitude and phase of QBlade and FLOWer is good.
The same conclusions as for the flapwise bending moment can be drawn for the
edgewise bending moment. However, the relative deviations between the
simulated curves of QBlade and FLOWer are larger.
To sum up, a good accordance was achieved for the absolute values and the
azimuthal distribution regarding the on-blade velocity and the AoA.
Consequently, the numerical setup of FLOWer can be seen as validated in
terms of these two parameters. Concerning the velocity planes, differences
between experiment and FLOWer occur but can be explained. The
comparison between the two FLOWer cases (with and without wind tunnel
walls) showed that in the present case the wind tunnel leads to a constant
offset between the curves for the on-blade velocity, the AoA and the bending
moments. Regarding the QBlade results, the on-blade velocity, as well
as the amplitude and phase of the AoA can be seen as validated by the
experiment, too. As the AoA distribution of QBlade lies on the far
field solutions of FLOWer, the differences in the mean values of the
AoA can be attributed to the absence of wind tunnel walls in the
QBlade predictions. The offset between the QBlade and FLOWer
wind tunnel cases regarding the bending moments is not only a result of the
neglect of the walls but is also influenced by the set of airfoil polars
used in the LLFVW simulation.
In a next step, in order to better match the experimental conditions,
simulations with unsteady inflow, considering the measured shear and
turbulence, will be performed. Moreover, experiments with passive and active
load control will be performed and compared to simulations of both
QBlade and FLOWer. Thereby, QBlade will be used for
dimensioning purposes of the flaps prior to the experiments. Afterwards, the
most promising configurations will be investigated numerically on a full size
turbine using QBlade and FLOWer, where the LLFVW code can
be used for the preliminary design, and the CFD code for the closer
look into the aerodynamic details.