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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)𝑑𝐴

𝑐𝑠

𝑐𝑣 (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 = ∑ �̇�𝑉𝑜𝑢𝑡 − ∑ �̇�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

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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= 𝟐𝑭𝑫

𝝆𝒗𝟐𝑨 [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.

I:̅ 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]

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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

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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

y

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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

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6.5 Result & discussion Cylinder Square Tower model

C.V.

method(mN)

3.10 4.39 1.24

𝐶𝑑 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 𝐶𝑑 𝑚𝑒ℎ𝑜𝑑)

𝐹𝑜𝑟𝑐𝑒 𝑓𝑟𝑜𝑚𝐶𝑑 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

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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