Wave force measurement on different shapes of wind turbine tower structures.

1. 1
WAVE FORCE MEASUREMENT ON DIFFERENT SHAPES OF WIND TURBINE
TOWER STRUCTURES
KAGGWA ABDUL
Dept. Mechanical Engineering
National Chiao Tung University
kaggwaabu@ymail.com
Yi-Xian Zheng
Dept. of Power Mechanical Engineering
National Tsing Hua University
ytapjqmp@gmail.com
1. ABSTRACT
An experiment was carried out to study wave force measurement
on different shapes of a wind turbine tower (cylinder, square rod
and tower modal). The water tunnel LW-9174 was used for
testing designed models fixed at the bottom in a streamline.
Several photos were taken for PIV analysis to study the velocity
profile and flow direction. Reynolds number was calculated to
define the regime of the flow and finally drag force was
determined by use of force measurement methods.
Keywords: Force measurement, PIV, Drag force.
2. INTRODUCTION
A wind turbine is a Mechanical device that produce electric
power from the wind [1]. Recently, interest in the development
of renewable energy is increasing due to the exhaustion of
natural resources; renewable energy is now an essential study
topic for economic development. A faster wind speed is
observed in coastal areas than in inland areas. Therefore,
offshore or coastal areas haves better conditions for the
development of wind energy, because the electricity of wind
power is in proportion to the cube of the wind speed. Europe is
the world leader in offshore wind power, with the first offshore
wind farm being installed in Denmark in 1991[2]. Due to the
significant capacity of power generated by offshore wind
turbines, research has been carried out around the world
especially the offshore wind turbine tower is one of the core
technologies in the offshore wind energy field [3-4]. Several
types of wind turbine towers are possible, such as mono-pile,
suction caisson, and tripod and tetra pod caissons. In comparison
with onshore turbines, the foundations of offshore turbines must
support a taller tower due to the additional height required with
the depth of water. Furthermore, the Withstanding forces and
overturning moments caused by waves and currents should also
be considered. The calculation of complex external forces that
affect the wind turbine tower are carried out for the planning and
designing of an offshore wind farm.
3. FORCE MEASUREMENT
3.1 Momentum conservation of control volumes.
Momentum conservation is a widely used concept in fluid
mechanics. This concept can be used to derive fluid dynamics
equation in a flow field and obtain results. The conservation of
linear momentum for a system is
𝑑
𝑑𝑡
(𝑚𝑉)𝑠𝑦𝑠 = ∑ 𝐹𝑠𝑦𝑠 [5]. (1)
Bringing concept of control volume into (1). This equation will
turn into
∑ 𝐹𝑠𝑦𝑠 = ∑ 𝐹𝑐𝑣 =
𝑑
𝑑𝑡
∫ 𝜌𝑑𝑉 + ∮ 𝜌𝑉(𝑉 ̇ 𝑛)𝑑𝐴𝑐𝑠𝑐𝑣
(2)
In this case, flow field is assumed to be steady so density will
not change by time. The time differential term can be neglect.
The remaining term of control surface is equivalent to sum of
momentum at each control surface. This difference of
momentums represents forces acting at the control volume. As
a result, one simple equation can be derived as
𝐹𝑐𝑣 = ∑ 𝑚̇ 𝑉𝑜𝑢𝑡 − ∑ 𝑚̇ 𝑉𝑖𝑛 (3)
By using this equation and velocity profile obtained from
velocity measurement results, forces acting on the model (Fig.
1) can be easily be calculated.
Fig. 1 Schematic of momentum conservation in control volume
3.2 Drag coefficient method
Another method to calculate drag force is by determining drag
coefficient. Drag is the component of a force acting on a body
that is projected along the direction of motion.
Fig. 2 Drag force on a testing model

2. 2
Drag force is influenced by many factor such as property of
working fluid, flow speed, geometry of models, and so on.
Scientist obtained a dimensionless coefficient called drag
coefficient. This can represent the characteristic behavior at
different geometry models. The bigger the drag coefficient is, the
larger the drag force will act on the model despite in the same
condition. Drag coefficient is also affected by Reynolds number
and model geometry [6-7]. Reynolds number is the ratio of initial
to viscous forces and it is used to define the regime flow type of
a fluid whether laminar, transitional or turbulent. In this
experiment, Reynolds number can be carried out because the
diameter of testing models and the velocity in flow field are
known. Using the graph below (Fig. 3.1, 3.2), drag coefficient
(CD) can be approximated. This formula Cd=
𝟐𝑭 𝑫
𝝆𝒗 𝟐 𝑨
[8] can easily
be used to calculate the drag force (FD) where ρ is density of
working fluid, v is fully-developed speed in flow field and A is
frontal area. After calculation, the results from momentum
conservation and drag coefficient method can be compared.
Fig. 3.1 Drag coefficient at different Re of a sphere
(Courtesy of NASA: Drag sphere)
Fig. 3.2 Drag coefficient at different shape
(Courtesy of Wikipedia: Drag coefficient)
4. PARTICLE IMAGE VELOCIMETRY (PIV)
Particle Image Velocimetry is a flow-field technique providing
instantaneous velocity vector measurements in a cross-section of
a flow field (in water or wind tunnel). The use of modern digital
cameras and dedicated computing hardware, results in real-time
velocity maps. PIV can produce 2D and 3D velocity vector fields
compared to other flow measurement techniques (laser Doppler
velocimetry and hot-wire anemometry) that measure velocity at
only a single point at a time. The flow filed is illuminated by
laser sheet in the target area so that seeded particles are visible
and the sensor array of a digital camera is able to capture each
light pulse in separate image frames. A simple digital camera is
used to capture a bunch of photos continuously at a given time
interval (∆t). The relation between two images can be obtained
by cross-correlation equation [9] as below. After particle
displacement (∆x) is carried out and speed equals to
displacement divide by time interval. The velocity magnitude
and vector is now known.
r (u, v): Function of flow field at u and v direction.
i, j: Total number of offset nodes.
I: Gray scale of each nodes in the whole image.
I̅: Average gray scale of the whole image.
M: Gray scale of each nodes in the interrogation window
M̅: Average gray scale of the interrogation window.
PIVlab is used as a software to analyze photos carried out
throughout this experiment. The cross-correlation method is
based on Fast Fourier Transform (FFT). Interrogation window is
48 pixels. Step is 24 pixels. Vector validation is used manually.
Thirty images a set for PIV analysis, velocity profile is
calculated.
Fig.4 Laser Optical Measurement Systems and Sensors
Courtesy of Dantec dynamics [10]

3. 3
5. EXPERIMENTAL SETUP
5.1 Water tunnel
In order to measure forces acting on a wind turbine tower, a
downstream environment is carried out in this study. In our
research, we used LW-9174 closed circuit water tunnel as our
testing environment [11]. Depth and velocity of the flowing fluid
can be adjusted. Testing object can be attached on a side-wall
base which is designed by the manufacturer. We can put a model
to be tested in the flowing water, and use the laser of LW-9174
to do particle tracing for flow visualization. PIV (Particle image
velocimetry) technique can be also used with LW-9174 and an
additional digital camera to obtain instantaneous velocity
measurements.
Table. 1 Specifications of water tunnel LW-9174.
5.2 Testing models
We considered a monopile type model as our testing model
object. The real height of wind turbine tower is 60 m [12]. The
selected scale down ratio is 1:600.The reason is to make the
tower model appear above the depth of water in the tunnel and
the diameter is 25mm. We used three testing model shapes
namely; cylinder, square rod and the tower model as
demonstrated at Fig. 5.
Fig. 5 Models Geometry
A digital camera is fixed and focusing downward toward the
streamline so as to capture clear photos that where later analyzed
by PIV software. Laser (300Mw) was projected horizontally in a
position where it can illuminate the fluid with the testing model
in the wind tunnel. The testing model with a cylindrical shape is
positioned vertically (z-axis) in the flowing fluid inside the water
tunnel. The setup schematic and positions of each device are
shown as Fig. 6.1 Fig. 6.2.The system was run for a couples of
minutes so as the fluid to stabilize (uniform velocity) before the
photos and calibration of force were done.
Fig. 6.1 Schematic of setup
Fig. 6.2 Experiment setup
Testing section
Width x Height x Length 16 x 25 x 75 (cm)
Velocity 0.05 ~ 2 m/s
Water depth Adjustable
x y
z

4. 4
6. VELOCITY MEASUREMENT
6.1 Layer division strategy.
In this experiment, laser sheet can only be projected at single
depth. In other words, velocity profile at different depth should
be calculated separately. As a result, layer cutting is important to
this experiment. For this control volume, four different layers are
defined. From layer1 to layer4, their height are 3.0, 6.5, 10.0 and
13.0cm respectively. The more layers the better result can be
obtained. However, more layers mean more time on experiment.
For this experiment, only four different layers are cut as Fig. 7
shown.
Fig. 7 Layer cutting schematic
6.2 Control volume and surface partitioning
Before using momentum conservation in a control volume,
control volume must be defined first. The control volume is a
16x8x13(cm) space. First, length (16cm) is determined by the
distance between inlet and outlet surface. After flow passing
through a model, circulations will be produced. This may cause
errors on drag force calculation. A better result can be gotten
when the flow field behind the model become more stable. By
choosing a further distance behind the model satisfy this
demand. Second, width (8cm) is determined for the
consideration of boundary layers. Velocity profile in boundary
layers may have lots of errors and large difference. To avoid
these errors, choosing fully-developed area as a control volume
is a solution. Third, depth (13cm) is determined because the
height of these three models are almost the same (~13cm).
After defining the geometry of control volume, assuming that
flow only travel at one direction. Only inlet and outlet control
surface should be considered under this simplification. Also,
notice that momentum conservation equation Eq. (3) is in a
summation form. The velocity at different location of control
surface must be calibrated. A new partition strategy is used. For
width direction, 50 partitions will be divide by PIVlab. And for
depth direction, 4 partition will be divide by different depth
observation. So, there’re totally 200 cells (Fig. 8) on the control
surface, each has its own inlet or outlet speed.
Fig. 8 Control surface partitioning
6.3 Calibration
Before carrying out the experiment, calibration is an important
step to examine the devices for this research. There’re lots of
factors that may interfere the data, doing calibration can help us
figure out if uncertainty is strong or not.
The laser sheet will be projected at the middle depth of water
tunnel. No model is in the tunnel, too. In this way, pure velocity
profile can be obtained. By choosing a random fully-developed
area as Fig. 9, the area mean velocity can be carried out. Do
calibrations for five times to observe mean velocity difference
as Table. 2 shown. From this results, the average is
0.04272(m/s), deviation is 0.000767(m/s) and uncertainty is
1.8%.
Fig. 9 Random choice fully-developed area to measure mean
velocity
Table. 2 Mean velocity at randomly chosen area
Exp No. 1 2 3 4 5
Speed(m/s) 0.0430 0.0417 0.0435 0.0422 0.0433
x

5. 5
6.4 Velocity map (x-y)
After PIV analysis, vector profile of each model can be shown
using the PIVlab. Calculate mean vector from 30 images and
draw the velocity magnitude color plots. As Fig. 10.1 shown.
From left side to right side are cylinder, square rod and tower
model. The red color means high speed area, blue for low speed.
There’re models and its shadow at the red color area. Doing PIV
analysis will cause some errors. So putting a mask there can
block PIV analysis. The 4 blue star dot in each profile is the
boundary of control volume. The upper two dots form one line
which is outlet control surface. Bottom dots form one line
represent inlet control surface. Profile missing parts become to
the blue squares, it’s caused by the dust floating on the water
surface. Despite of a free surface on the test section, the speed is
too slow to cause movement on the surface.
For cylinder model, after passing through the model, velocity
drop a lot behind the model. S-shape stream lines are resulted
from boundary separation. Circulations and vortex shedding also
occur behind the cylinder model. When the model becomes to
the square rod, same phenomenon appear but more serious.
Velocity decay much more after passing through the square rod.
Unsteady circulation and flow almost occupy the outlet regions.
Discussion of unsteady condition will be issued later. For tower
model, circulations and vortex seems be weaker. This is because
its diameter is smaller than the other two. The circular shape can
avoid strong boundary separations, too.
From Fig. 10.1, an obvious difference profile can be observed.
The biggest momentum change is in square rod model testing.
The smallest momentum change is in tower model. A prediction
of drag force can be made: the largest drag force will be acting
on square rod. Value of drag force will be discussed later.
Though the planer profile is important, cross section profile is
important, too. Fig. 10.2(next page) is the velocity profile at y-z
plane. The flow direction is parallel to the direction normal to
this paper. Red color mean high speed area, blue mean low speed
area. Upper three images are the inlet profiles for each model.
The bottom three images are the outlet profile. Different models
are put in order from left side to right side.
Obviously, the inlet profile are all uniform. Just a little error
when doing PIV analysis. After passing through the models,
velocity decay no matter what depth it is. The biggest drop is
occur at the square rod model. The smallest drop is happened at
the tower model. It’s the same result as x-y plane profile. From
these six images, it seems no relationship between the depth and
the velocity. But at initial test, boundary layer thickness is about
4cm which will include layer1. So there may be some errors at
the layer1. The momentum difference will become lower due to
the boundary layer drag effect. Final, calculated the momentum
difference between inlet profile and outlet profile, forces acting
in the control volume can be carried out in the next part.
Cylinder model Square Rod model Tower model
Fig. 10.1 Velocity maps of different type models (x-y plane)
x
y

6. 6
6.5 Result & discussion
Cylinder Square Tower model
C.V.
method(mN)
3.10 4.39 1.24
𝐶 𝑑
method (mN)
2.54 3.36 1.14
Error (%) 22.33% 30.82% 8.92%
Table. 3 Forces acting on models by different method
After calculating the momentum difference, drag forces are
obtained as shown in Table. 3. The first row is by control volume
method, where velocity profile results are obtained from PIV
analysis. The second row is obtained by drag coefficient equation
3.2 drag coefficient method. Values gotten from drag
coefficient method are consider as ideal forces. Hence,
experimental and ideal forces can be used to obtain errors. Error
(%)=
(𝐹𝑜𝑟𝑐𝑒 𝑓𝑟𝑜𝑚 𝐶.𝑉.𝑚𝑒𝑡ℎ𝑜𝑑)− (𝐹𝑜𝑟𝑐𝑒 𝑓𝑟𝑜𝑚 𝐶 𝑑 𝑚𝑒ℎ𝑜𝑑)
𝐹𝑜𝑟𝑐𝑒 𝑓𝑟𝑜𝑚𝐶 𝑑 𝑚𝑒𝑡ℎ𝑜𝑑
× 100%.
Clearly, all values calculated by C.V. (control volume) method
are larger than those of drag coefficient method. One explanation
is that the circulations obtained at the outlet area. Fig. 10.1,
shows non uniformity of flow that is not following the x-
direction. In other words, some flow may exit from the side
surface of control volume. Precisely, momentum will be lost
from the side control surface. It cause the momentum change
bigger than expected, so the forces acting in the control volume
are over-estimated. Furthermore, the square rod cause the
strongest circulations. It gives an explanation that is why the
error (%) in the square rod is much bigger.
Besides, force acting on the model body is direct ratio to the
frontal area towards the flow. It’s unfair to compare pure forces
between each model. Let the forces from C.V. method divide by
frontal area as shown in Table. 4. These 3 values equals to 3
different forces acting on a unit frontal area. In other words, this
concept is like “pressure”. In this way, it’s easy to observe the
effect of geometry or shapes. The pressure acting on square rod
is the bigger compared to other tested modals because its shape
is too sharp and rough. While the PIV analysis may produce
some errors, or else pressure acting on cylinder and tower must
be the same in the ideal situation
Cylinder Square rod Tower
Force per
frontal area (Pa)
0.936 1.351 0.734
Table. 4 Forces acting per frontal area on different models
Fig. 10.2 Velocity maps of different type models (y-z plane)
Cylinder inlet Tower inlet
Cylinder outlet Square rod outlet Tower outlet
Square rod inlet z
y
Layer 1
Layer 2
Layer 3
Layer 4
Layer 1
Layer 2
Layer 3
Layer 4

7. 7
6.6 Vorticity map
Vortex and circulations cause huge errors to the momentum
difference. The outlet speed is lower-estimated. This is resulted
from the flow that may have passed on side surface of the whole
control volume. So there is momentum loss from side surface.
That’s why the values calculated by PIV analysis are lower than
drag efficient method.
Take a look at Fig. 11, there’re vorticity maps of three different
models. Vorticity is an important value that can help us to figure
out whether circulation is strong or weak in a specific area. When
the value is close to zero, it means more circulation occur. On the
contrast, when it becomes very large or small, it means
circulations are strong.
7. CONCLUSION
The geometry shape of the tower determines the wave force
exerted on a tower as we saw that spherical structures like in our
case cylinder and the tower registers less force compared to the
square rod. Smooth and smaller structure provide a small drag
force. Whereas, rough structures yield large drag force.
Increasing tunnel width or decreasing characteristic length will
enhance the quality of analysis. PIV technique provides a perfect
study of velocity profile and the direction of particles around
cylinder, square rod and tower modal tested and this gives a good
comparison between different shapes.
8. Acknowledgement
We would like to take this opportunity to thank Dr. Chihyung
Huang from the department of Power and Mechanical
Engineering NTHU for the great advises and ideas he’s been
always contributing towards this project.
9. REFERENCES
1. http://en.wikipedia.org/wiki/Offshore_wind_power
2. The European Wind Energy Association (EWEA) report,
2011
3. Global Wind Turbine Tower Industry journal, 2012.
4. Architectural Institute of Korea (2009). Korean building
code, Korea. Byrne, B. W. and Houlsby, G. T. (2006).
5. Conservation of Momentum using Control Volumes,
http://www.mne.psu.edu/cimbala/learning/fluid/cv_momen
tum/home.htm
6. Drag of a sphere, http://www.grc.nasa.gov/k-
12/airplane/dragsphere.html
7. Drag coefficient,
http://en.wikipedia.org/wiki/Drag_coefficient
8. Drag coefficient, www. Engineering toolbox.com/drag-
coefficient.
9. C. Meinhart, S. Wereley and M. Gray, “Volume
illumination for two-dimensional particle image
velocimetry,” Measurement Science and Technology, vol.
11, p.809, 2000
10. http://www.dantecdynamics.com/measurement-principles-
of-piv
11. Long Win LW9174 閉迴路水洞操作使用說明書
12. Da Chen, Kai Huang, Valentin Bretel and Lijun Hou,
“Comparison of Structural Properties between Monopile
and Tripod Offshore Wind-Turbine Support Structures”.
Fig. 11 Vorticity map of 3 different models
x
y