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Prediction of the wind field in moderate terrain
using the Navier-Stokes solver WindStation
Antonio M. Gameiro Lopes1
Omar Herrera Sánchez2, Herbert Koch2, Regina Daus2, Thomas Sperling2, Rhea Braun2
1Dep. de Eng. Mecânica (FCTUC – Polo II) – Universidade de Coimbra 3030-201 Coimbra, Portugal,
antonio.gameiro@dem.uc.pt
2EuroWind GmbH, Robert-Perthel-Str. 19, D-50739 Köln, Germany, gutachter@eurowind.info
Summary
The CFD model (Computational Fluid Dynamics) WindStation was developed for the simulation of the three-
dimensional flow in variable terrain. The implemented forest model and the possibility to adjust the thermal strati-
fication, offer tools to adapt for complex flow situations. WindStation is used to simulate the wind fields at two
wind farm sites in Germany, where overlapping wind time series are available. One wind data set is used as the
meteorological input for WindStation while the second serves for the independent validation of the calculated wind
fields. The simulation results show a very good reproduction of measurements even for a large modelling domain.
1. Introduction
Especially in Germany, wind park planners focused
on areas in the low mountain range during the last
few years. At those sites, an accurate prediction of
wind characteristics is a demanding challenge due
to the complexity of the physical phenomena in-
volved. The solutions provided by simple kinematic
(mass-conservative) solvers do not take into ac-
count non-linear phenomena associated with the
flow behaviour over mountainous topography in
conjunction with roughness variabilities. Computa-
tional fluid dynamics (CFD) models are appropriate
to simulate wind fields in such a complex terrain. In
this work, the CFD software WindStation is validat-
ed at two sites in moderate terrain by using different
measured wind data sets.
2. CFD Software WindStation
The solver Canyon which is implemented in Wind-
Station [1] solves the fluid dynamics equations
(Navier-Stokes equations) [2] coupled with different
variants of the k-ε turbulence model [3]. Thermal
effects are taken into account by solving the energy
conservation equation. The implemented forest
model provides turbulence and momentum source
terms in order to simulate the effect of large rough-
ness elements. The inclusion of Coriolis forces
prevents the continuous downstream growing of the
atmospheric boundary layer, preserving the possibil-
ity of simulating wind fields for large areas. Wind-
Station is implemented in a graphical interface ori-
ented towards an easy and intuitive utilisation. Fur-
thermore, import and export functions for the soft-
ware WindPRO and Microsoft Excel are included.
3. Description of Case Studies and Input data
WindStation has been validated in several wind
farm projects in Germany, Portugal and Poland. In
this paper, two of these case studies are presented.
3.1 Digital Terrain Data
For both case studies digital SRTM data (Shuttle
Radar Topography Mission) of the NASA are used.
The original resolution of three arc seconds is inter-
polated to the target solution of 50 m and 200 m for
Case Study 1 and Case Study 2 respectively.
3.2 Case Study 1
The area of Case Study 1 is located in the federal
state of Thuringia in Eastern Germany featuring a
moderate terrain structure with smaller forested
areas. The input digital elevation model (DEM) and
roughness data are visualised in Fig. 1. Almost
thirteen months of an overlapping time series of
wind speed and wind direction are available for this
case study.
One was measured by a LiDAR device located
close to a forest and the second by anemometers
Fig. 1: Visualisation of the DEM and roughness
length data of Case Study 1 with locations of the
LiDAR and WMM.
LiDAR
WMM
LiDAR
WMM
m
LiDAR
WMM
m a. NN
installed at a wind met mast (WMM) located close to
some buildings. The distance between these loca-
tions is about 25 km. The wind speed time series of
the WMM top-level anemometer with a resolution of
10 min was filtered. Time steps with a measured
wind direction of 60°±1°, which corresponds to the
orientation of the two measurement systems to each
other, were used as input for the wind field simula-
tion. Corresponding data measured by the LiDAR
served to validate the simulated mean vertical wind
profile. The data of the two measurement systems
are not long-term referenced.
3.3 Case Study 2
The area of Case Study 2 is located in the federal
state of Hesse in Central Germany. The area has a
complex terrain structure with forests. At the site
there are two months of overlapping time series
available – one measured by a SODAR device and
one with a WMM which was installed in a forest.
The distance between the two locations is 0.7 km.
Directional mean wind speed data of the WMM top-
level anemometer without a long-term correction is
used as input for the wind field simulation with
WindStation. Deviating from Case Study 1, not only
one wind direction sector is simulated but 36.
WindStation has the capability of automatically
aligning the calculation domain with the incident
wind direction (Fig. 2). This procedure aims at keep-
ing numerical discretisation errors as low as possi-
ble. The wind data measured by the SODAR device
is used to validate the modelling results.
4. WindStation Settings
The forest model is activated with zf/z0=20 and
CdxLAD=0,1 where zf is the mean forest height, z0
is the roughness length and CdxLAD characterises
the forest density (product of drag coefficient and
leaf area density. The atmospheric stability is set to
neutral for both case studies. Coriolis effects are not
taken into account. The horizontal resolution is
constant all over the domain with 200 m for
Case Study 1. This comparatively high value was
chosen to reduce calculation time. For Case Study 2
a mesh spacing of 50 m is used. The vertical resolu-
tion of Case Study 1 is visualised in Fig. 3.
In the vertical plane, levels are distributed by an
expansion factor ensuring a higher resolution near
the ground. The number of vertical levels was 30 for
Case Study 1 and 50 for Case Study 2. For both
cases, the domain top was placed at an altitude of
3’500 m and input correction was activated. This
feature dynamically adjusts the boundary layer
profile at the upstream boundaries aiming at a
match between the simulated wind speed and direc-
tion and the input wind data at the top level.
5. Results
5.1 Case Study 1
The upper part of Tab. 1 shows the comparison of
the simulated wind speeds at the location of the
WMM, which served as the input and the measured
(and filtered) wind time series as absolute and rela-
tive differences.
WMM (input)
height
a. g. [m]
meas.
[m/s]
sim.
[m/s]
diff.
[m/s]
diff
[%]
99.0
4.69
4.69
0.00
0.00
96.0
4.67
4.67
0.00
0.00
80.0
4.51
4.54
0.03
0.67
60.0
4.31
4.34
0.03
0.70
LiDAR (distance of 25 km to WMM)
101.5
4.97
4.92
0.05
1.01
81.5
4.76
4.75
0.01
0.21
61.5
4.49
4.55
-0.06
-1.34
Tab. 1: Comparison of simulated and measured
mean wind velocities of Case Study 1 at the position
of the WMM (input) and the LiDAR device (valida-
tion).
Fig. 2: Visualisation of the modelling domain (light
red: simulation domain, dark red: results domain),
which is rotated in each simulation run of
Case Study 2 in WindStation. Exemplary for the
locations of the two measuring devices, the site of
the WMM is shown as a black dot.
Fig. 3: Visualisation of the vertical mesh spacing of
the calculation domain in WindStation for
Case Study 1.
N
WMM
As expected, due to the input correction, simulation
results perfectly match the input data at the top level
(and also at the redundant anemometer). For the
lower anemometers the differences show values
between 0.67 % and 0.70 %.
The comparison with LiDAR measurements summa-
rised in the lower part of Tab. 1 shows rather small
differences with values between 0.21 % and
-1.34 %.
In Fig. 4 the simulated wind field at 99.0 m height
above ground is shown in colour contours. Blue
colours correspond to lower wind velocities, which
can be found mainly in the area of the valley in the
east of the modelling domain. With WindStation,
simulations can be performed for an expanded
model domain. In this area, which is indicated with a
grey rectangle in Fig. 4, results cannot be exported
but the influence of the terrain on the wind field is
considered. This means that the WMM and LiDAR
are located in sufficient distance to the actual inflow
boundary layer.
5.2 Case Study 2
In Tab. 2 the mean simulated and measured wind
speeds at the locations of the WMM and the
SODAR device are compared. The WMM top level
served as the input wind speed. Due to input correc-
tion, 0.00 % difference between measured and
simulated values are found at the top level. Also the
59.0 m level is simulated with a 0.00 % difference
compared to the measured value.
In the lower part of Tab. 2 the measured and simu-
lated wind speeds of the SODAR device can be
found. The differences amount to between 0.25 %
at 60.0 m height above ground and 2.25 % at
120.0 m height above ground.
WMM (input)
height
a. g. [m]
meas.
[m/s]
sim.
[m/s]
diff.
[m/s]
diff
[%]
101.0
4.58
4.58
0.00
0.00
59.0
3.55
3.55
0.00
0.00
SODAR (distance of 0.7 km to WMM)
120.0
4.33
4.30
0.03
0.69
100.0
3.94
3.93
0.01
0.25
60.0
3.11
3.04
0.07
2.25
Tab. 2: Comparison of simulated and measured
mean wind velocities of Case Study 2 at the position
of the WMM (input) and the SODAR (validation).
Fig. 5 shows a close-up of the simulated wind field
for the 0° inflow direction at 101.0 m height above
ground around the locations of the different measur-
ing devices of Case Study 2. The wind field is
shown as a transparent overlay on a satellite image
from Google Earth Pro. The locations of the meas-
uring devices are given as black dots assigned with
the terrain elevation above NN.
6. Discussion and Conclusion
The available filtered wind statistics of Case Study 1
could be reproduced very well at the locations of the
WMM and the LiDAR. As the domain of
Case Study 1 is very large, simulations were not
performed for a large amount of wind directions like
for Case Study 2. This is a task for future work. It
cannot be said for sure that the reproduction of a
complete wind statistic will produce equally excel-
lent results. Nevertheless, the CFD software Wind-
Station offers settings (consideration of Monin-
Obukhov length and Coriolis force) to adjust the
Fig. 5: Close-up of the simulated wind field at
100.0 m height above ground for Case Study 2 as
transparent overlay of a satellite image from Google
Earth Pro. The Locations of the WMM and the
SODAR are indicated by black dots. They are as-
signed with the elevation above NN. The inflow and
north direction are indicated by black arrows.
Fig. 4: Wind field colour contours at 99.0 m height
above ground as simulated by WindStation for
Case Study 1. The locations of the WMM (input)
and LiDAR (validation) are marked as black dots.
The inflow and north direction are indicated by
black arrows.
5.0
4.8
4.6
4.4
4.2
4.0
3.8
3.6
3.4
3.2
3.0
v [m/s]
WMM
LiDAR
N
inflow
inflow
5.6
4.5
4.4
4.3
4.2
4.1
4.0
3.9
3.8
3.7
3.6
v [m/s]
SODAR
305 m
WMM
357 m
N
model in case the simple assumption of a neutrally
stratified atmosphere without Coriolis effects does
not hold.
For Case Study 2 the reproduction of the mean wind
speed represented by 36 inflow situations and the
validation with the SODAR device showed very
good results. Considering the complex terrain and
the different measuring techniques the deviations
between measured and simulated mean wind speed
are very small.
As the overlapping time series are very short it was
not feasible to generate a representative wind
statistic (frequency distribution) for Case Study 2. In
WindStation the simulation of wind fields by using
wind statistics in TAB-format as input wind speed is
possible. The software generates representative
inflow situations by considering a specified amount
of wind direction sectors and wind speed classes.
7. Outlook
With the simulation of wind fields and vertical wind
profiles using the CFD software WindStation, this
paper placed emphasis on tasks which arise in the
context of wind and energy yield assessments. With
its implemented variants of the k-ε model and the
possibility to adjust the parameters of the turbulence
model as well as the forest model, WindStation
offers possibilities in simulating the turbulence in-
tensity (TI) precisely. Furthermore the correction of
simulated TI by using a quotient method based on
site specific data is implemented. Therefore Wind-
Station also provides tools for turbulence site as-
sessments which serve as a base for load calcula-
tions performed by turbine manufacturers. Thus
future work will concentrate on the simulation and
validation of turbulence data.
8. References
[1] Lopes, A. M. G. - "WindStation - A software for
the simulation of atmospheric flows over complex
topography", Environmental Modelling & Software,
Vol.18, N.1, pp. 81-86, 2003
[2] Lopes, A.M.G., Sousa, A.C.M., Viegas, D.X.,
“Numerical Simulation of Turbulent Flow and Fire
Propagation in Complex Terrain”, Numerical Heat
Transfer, Part A, N. 27, pp. 229-253, 1995.
[3] Lopes, A. M. G.: WindStation Version 1.0.0 –
User’s Manual. Coimbra, 2017.
Acknowledgments
This paper was written in collaboration with the
Department of Mech. Engineering of the University
of Coimbra, Portugal and the company menzio
GmbH from Emden, Germany which is responsible
for the sale and distribution of the software Wind-
Station. The data used for the presented case stud-
ies was provided by VSB Neue Energien Deutsch-
land GmbH from Dresden, Germany.
