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Master's Degree Thesis ISRN: BTH-AMT-EX--2011/D-09--SE
Supervisor: Ansel Berghuvud, BTH Dipl.-Ing. Mona Goudarzi, IPH,
Hannover
Department of Mechanical Engineering Blekinge Institute of
Technology
Karlskrona, Sweden
2011
Abtin Namiranian
3D Simulation of a 5MW Wind Turbine
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3D Simulation of a 5MW Wind Turbine
Abtin Namiranian
Department of Mechanical Engineering
Blekinge Institute of Technology
Karlskrona, Sweden
2011
Thesis submitted for completion of Master of Science in
Mechanical Engineering with emphasis on Structural Mechanics at the
Department of Mechanical Engineering, Blekinge Institute of
Technology, Karlskrona, Sweden.
Abstract: In the present work, the influence of turbulence and
gravity forces on the tower and the rotor of a 5MW onshore wind
turbine has been investigated. A full geometry of the turbine has
been designed and simulated in a virtual wind farm and then the
fluid loads are imported into the structural part by fluid
structure interaction (FSI) method. The final results are shown
that the gravity force is significantly higher than turbulence
loads and should be considered in designing of the large wind
turbines.
Keywords: Wind turbine, Turbulence and gravity loads,
Computational Fluid Dynamics, Finite Element Method, Fluid
structure interaction, ANSYS
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Acknowledgements
This thesis is the final project for the Master of Science in
Mechanical Engineering with specialization in structural mechanics
at the Department of Mechanical Engineering, Blekinge Institute of
Technology, Karlskrona, Sweden.
This work has been performed at Institut für Integrierte
Produktion Hannover gGmbH (IPH) under supervision of Dipl.-Ing.
Mona Goudarzi.
I would like to express my sincere appreciation to Dipl.-Ing.
Mona Goudarzi for her encouragement, support and guidance through
all my work. I am also grateful to Dr. Ansel Berghuvud at the
department of Mechanical Engineering at Blekinge Institute of
Technology for his support and suggestions.
Finally, special thanks to my parents who have always supported
and inspired me throughout my academic life.
Hannover, August 2011
Abtin Namiranian
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Contents
1. NOTATION 5 2. INTRODUCTION 7
2.1 BACKGROUND 7 2.2 AIM AND SCOPE 8
3. WIND TURBINE CONCEPTS 9 3.1 MODERN WIND TURBINE 9 3.2 WIND
FARMS 11
4. WIND TURBINE COMPONENTS 13 4.1 ROTOR 14 4.1.1 Rotor Blades
14
4.1.1.1 Aerodynamics of Rotor Blades 14 4.1.1.2 Airfoils 14
4.1.2 Wind Power 18 4.1.3 Rotor Power and Torque 19 4.1.4 Rotor
Design 20 4.1.5 Rotor Blades Material 24 4.1.6 Rotor Hub 25
4.3 NACELLE 25 4.4 TOWER 27
5. WIND TURBINE LOADS 29 5.1 AERODYNAMIC LOADS 30 5.2 GRAVITY
LOADS 30 5.3 CENTRIFUGAL LOADS 31 5.4 GYROSCOPIC LOADS 31 5.5 WIND
TURBULENCE 32 5.6 WIND SHEAR 32
6. THEORY 35 6.1 FINITE ELEMENT METHOD (FEM) 35 6.2
COMPUTATIONAL FLUID DYNAMICS (CFD) 36 6.2.1 Governing equation
36
6.2.1.1 Mass conservation 36 6.2.1.2 Newton's second law 37
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6.2.1.3 Energy equation 37 6.2.1.4 Navier-Stokes equations
38
6.2.2 Finite Volume Method 39 6.2.3 Turbulence modeling 41
6.2.3.1 The model 43 6.2.3.2 The model 43 6.2.3.3 The
Shear-Stress Transport (SST) model 44
6.3 FLUID STRUCTURE INTERACTION 45
7. SIMULATION 46 7.1 GEOMETRY 46 7.2 CFX 48 7.2.1 Mesh 48 7.2.2
Model set up 49
7.3 STRUCTURAL 52 7.3.1 Mesh 52 7.3.2 Model set up 54
8. RESULTS 56 9. CONCLUSION 64 10. FUTURE WORKS 65 11.
REFERENCES 66
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1. Notation
Area
Drag force coefficient
Lift force coefficient
Power coefficient
Design power coefficient
Dimensionless constant
Energy
Force
Acceleration of gravity
Height
Specific total enthalpy
Internal energy
Thermal conductivity
Turbulent kinetic energy
Mass
Rotational speed
Pressure
Power
Design power
Turbulence production
Output power
Radius
Drag force
Lift force
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Energy source
Kinetic energy source
Enthalpy energy source
Body forces Temperature
Torque
Velocity vector in Cartesian coordinates
Velocity
Wind shear coefficient
Turbulent dissipation rate
Specific dissipation rate
Angular rotor speed
Air density
Ω Angular velocity
Generator efficiency
Mean wind velocity
Standard deviation ration
Viscous stress
Viscous stress components
Dynamic viscosity
Turbulent viscosity
Tip speed ratio
Viscosity
Fluid property
Γ Diffusion coefficient
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2. Introduction
2.1 Background
The use of renewable energy sources has increased significantly
in the past decade due to the robust request for the sustainable
protection of our environment. Among these renewable energies, the
use of wind power has become the fastest growing energy technology
in the world [17]. This remarkable energy can be captured and used
to generate electricity by implementing wind turbines which have
changed considerably since their beginnings. Today the commercial
size of wind turbines covers from 0.3 MW up to 7.5 MW, as shown in
figure 2.1.
Figure 2.1. Growth in size of commercial wind turbine
designs
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The size of wind turbines is performing as the main rule for
capturing energy from the wind. In other words, we can produce more
utilizable energy with larger wind turbines due to higher wind
speed, lower airflow frictional resistance and bigger volume of air
which flows through the rotor. Therefore, most of the wind turbine
producers in the wind turbine technology are focused on
constructing the larger wind turbines. On the other hand, the cost
of labor, maintenance and construction of the wind turbines
increase with the size of each part, specially tower and rotor.
Hence, wind turbine manufacturers are also concentrating on
bringing down the price of the turbines themselves.
In order to catch more power from the wind and supply more
electrical energy, we need to build a bigger rotor which is the
most significant part of the wind turbines. However, this part
depends on the size and shape of tower which provides the safe and
reliable performance of turbines under a variety of wind
conditions. Therefore, the understanding of forces which appear in
the tower and the suitable selection of the material used are
considered as other main factors in designing the large wind
turbines.
2.2 Aim and scope
This work concentrates primarily on the simulation of one of the
biggest wind turbines in the world. The purpose of this simulation
is calculating the effect of turbulence loads from the wind on the
rotor, nacelle and the tower, and then computing the gravity force
in each part in order to find the stresses and deflections in the
tower and the rotor of the turbine.
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3. Wind Turbine Concepts
One of the significant technologies of the 20th century is the
wind turbine technology which offers cost-effective solutions for
generating the electrical energy due to eliminate the dependency of
the world on the fuel-based sources such as oil and gas. Therefore,
the wind turbine technology is produced electrical energy without
greenhouse effects or deadly pollution gasses [2]. The wind turbine
technology offers electrical energy with lower installation and
maintenance costs unlike the other energy sources.
In this project, a wind turbine is a machine which converts the
wind power into electricity power and does not to be confused with
another type of machine, Windmill which converts the wind’s power
into mechanical power.
3.1 Modern Wind Turbine
Modern wind turbines can be classified into two configurations
depending on the rotation axis of the rotor blades: horizontal-axis
wind turbines (HAWTs) and vertical-axis wind turbines (VAWTs), as
shown in figure 3.1.
Figure 3.1. Types of modern wind turbine
In recent years, most of the commercial wind turbines are the
horizontal axis wind turbines (HAWT) which have their axis of
rotation horizontal to the ground and almost parallel to the wind
flow. These types of turbines have some noticeable advantages such
as low cut-in wind speed and easy furling. In general, the power
output of HWAT is higher than vertical-axis
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wind turbines due to the better power coefficient in HWAT.
However, the generator and gearbox of these turbines are to be
located over the tower which makes its design more complex and
expensive.
Horizontal axis wind turbines can be classified as single
bladed, two bladed, three bladed and multi bladed, as it is shown
in figure 3.2. The HAWT single bladed are not widely used now, even
though they appear to save the cost of other blades owing to
savings materials. In order to balance the weight of the single
blades, they require a counterbalance on the opposite side of the
hub. In addition, they need higher wind speed to produce the same
power output which obtains by the three bladed HAWT. The two bladed
wind turbines almost have the same disadvantage of the single
bladed and they can capture slightly less energy than three bladed.
The multi bladed turbines are mostly used as ‘water pumping
windmills’ and they do not use for producing the electricity [7].
Therefore, most of the present commercial wind turbines have three
blades.
Figure 3.2. Classification of wind turbines
The horizontal axis wind turbines base on the orientation of the
rotor can also be classified into upwind and downwind. When the
wind flow hits the rotor before the tower and makes it to rotate
then it is called upwind wind turbine. The advantage of upwind
design is that the blades can be worked in undistributed air flow
but the wind forces turn the rotor in direction of wind [6]. Thus,
they need an extra active mechanism, yaw mechanism, to keep the
rotor (blades) against downwind. On the other side, in downwind
wind turbines, the wind hits the tower first and then hits the
rotor. Hence, the wind itself can keep the rotor in downwind
situation without any supplementary mechanism.
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In all the time, the wind direction is not steady and changes
fast, hence the upwind wind turbine yaws faster than downwind due
to having the active yaw mechanism. Figure 3.3 displays the upwind
and downwind wind turbines.
Figure 3.3. Upwind and downwind turbines
3.2 Wind Farms
Numerous wind farm projects are being constructed around the
world with both offshore and onshore developments in wind turbine
technology.
The onshore wind turbines (figure 3.4) are installed frequently
in upland in order to achieve the higher wind speeds. However, the
onshore wind turbines are not growing as fast as offshore wind
turbines due to some restrictions such as turbine noises and
limited availability of lands.
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Figure 3.4. Onshore wind turbines
The offshore (figure 3.5) wind turbines give us more power
output and operate more hours in each year compared with the same
turbines installed in onshore due to having higher and more
constant wind speeds in open areas [6]. Another advantage of using
the offshore wind turbines is having lower wind turbulence with
higher average wind speeds and receiving less acoustic noises from
the turbine [14]. On the other hand, onshore wind systems have some
other advantages which make them also to be significant such as
cheaper substructure, cheaper installation and access during the
construction period, cheaper integration with the electrical-grid
network and cheaper and easier access for operation and maintenance
[29].
Figure 3.5. Offshore wind turbines
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4. Wind Turbine Components
Today, most of the commercial wind turbines are horizontal axis
wind turbine with typically three blades [18]. The main subsystems
of a horizontal axis wind turbine, as shown in figure 4.1, can be
separated into the rotor which consists of the blades and the hub;
The nacelle which includes gearbox, drive train, control parts and
yaw system; The tower and the foundation which depends on type of
turbine, onshore or offshore and finally the balance of the
electrical system which is including cables, switchgear,
transformers, and possibly electronic power converters [1].
Figure 4.1. Major components of a horizontal axis wind
turbine
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4.1 ROTOR
The most important and outstanding part of a wind turbine is the
rotor which is composed of the hub and the blades. The rotor
receives kinetic energy from the wind flow and transforms it into
mechanical shaft power.
4.1.1 Rotor Blades
4.1.1.1 Aerodynamics of Rotor Blades Aerodynamic deals with the
influence of gas forces on the bodies when air or other gases
moving through them. During the development of wind turbine,
several research and enquires have been done in aerodynamic filed
in order to find the successful model.
4.1.1.2 Airfoils The cross-section of a wind turbine blade is an
airfoil which is used to generate mechanical forces due to motion
of fluid around the airfoil. The width and length of the blade
depend on the desired aerodynamic performance and the maximum
desired rotor power.
Airfoils parameters The major characteristics of an airfoil are
shown in figure 4.2. Different types of airfoils are used along the
blades in order to catch the energy from the wind. There are many
types of airfoils available in designing blades and they are
classified by the numbers which are specified from the NACA
(National Advisory Committee for Aeronautics). Figure 4.3
illustrates the three classes of the airfoils.
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Figure 4.2. Main parameters of an airfoil
For instance, an airfoil which is specified with four digits,
the first number indicates the maximum camber of the airfoil at the
chord line (in per cent of chord), the second number demonstrates
the location of the point of maximum camber from the leading edge
(in tenth of the chord) and the third and fourth numbers show the
maximum thickness (in per cent of the chord) [4].
Figure 4.3. Sample airfoils
Forces on an airfoil When an airfoil is located in a wind flow,
air passes through both upper and lower surfaces of the blade which
has the typical curved shape. This shape makes the air to travel
more distance per unit time at the upper side than the
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lower side. In other words, the air particles move faster at the
upper side of the airfoil.
According to the Bernoulli’s theorem, the variety of the speed
in upper and lower side of the blade is made the different pressure
on the upper and lower surfaces of the airfoil. Therefore, these
pressure differences in the airfoil will cause a force R (figure
4.4.) which is divided into two main components in x and y
directions as follows:
Lift force – is specified as a force which is vertical to the
direction of oncoming airflow. The lift force is outcome of the
unequal pressure on the upper and lower airfoil surfaces. The lift
force is given by
coefficient (4.1)
Drag force – is defined as a force which is parallel to the
direction of oncoming airflow. The drag force is due both to
viscous friction forces at the surface of the airfoil and to
unequal pressure on the airfoil surfaces. The Drag force ( ) equals
to
coefficient (4.2)
Figure 4.4. Airfoil lift and drag
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where is the density of air, V is the velocity of undisturbed
air flow, A is the projected airfoil area ( ) and , are the lift
and drag coefficients which can be found under wind tunnel
experiments. In the wind tunnel, the lift forces and the drag
forces of the fixed airfoil are measured by some transducers which
are located in the vertical and horizontal planes [4].
Lift and drag forces on an airfoil are influenced by the angle
of attack, , which is the angle between the undisturbed wind
direction and the chord of the airfoil [4]. For instance, the
effect of angle of attack on the lift coefficient of an airfoil
demonstrates in figure 4.5. As it is shown, the lift force
increases with and reaches to the maximum value at a certain angle
of attack (12 in this example). After this specific point, the lift
coefficient quickly decreases with further increase in due to
entering the airflow in turbulent region which separates the
boundary layers from the airfoil. Therefore, the drag force rapidly
goes up and lift force goes down at this region.
Figure 4.5. Effect of angle of attack on airfoil lift
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4.1.2 Wind Power
The kinetic energy of the wind can be written as:
(4.3)
where m is mass (kg) and V is speed ( ⁄ ). The volume of air
which flows through the rotor in HWAT turbines is cylindrical
(figure 4.6.) with the amount of mass which passes through the
rotor of turbine per second. Therefore, the energy per second can
be defined as:
4.4
4.5
where A is the cross-section area of the cylinder and equals to
.
Figure 4.6. Volume of air in front of the rotor
It should be mentioned that power is defined as the rate of wind
energy passes through an area per unit time which means:
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4.6
4.1.3 Rotor Power and Torque
In reality, a wind turbine cannot derive all the wind power from
wind stream when it passes through the rotor of the wind turbine,
which means that some parts of kinetic energy of the wind is
transferred to the rotor and the rest of the energy leaves the
rotor. Therefore, the amount of wind energy which is converted to
the mechanical power by the rotor is defined as the efficiency that
is usually termed as the power coefficient, . The power coefficient
of the rotor can be explained as the ratio of power output from the
rotor to the accessible power of the wind in theory [4] which is
defined as:
2 4.7
where is the power output of the wind turbine. The power
coefficient of a turbine relies on many factors such as rotor
blades profile, blade arrangement, and blade setting, etc.
In order to find the torque of the rotor, we need to define the
thrust force by the rotor which can be expressed as:
12 4.8
Hence, the torque of the rotor will be:
12 4.9
where R is the radius of the rotor.
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The torque of the rotor, in reality, is less than this value and
is expressed in terms of the torque coefficient which is defined as
the ratio between the actual torque and the theoretical torque;
hence this coefficient is explained by:
2 4.10
where is the actual torque developed by the rotor. In order to
find the efficiency of interaction between the rotor and the wind
stream, another significant factor should be described as the ratio
between the velocity of the rotor tip and the wind velocity, which
is called tip speed ratio:
Ω 2 4.11
where Ω is the angular velocity and N is the rotational speed of
the rotor. In addition, the torque coefficient and the power
coefficient can be changed by the tip ratio as it is expressed:
Ω 4.12
4.1.4 Rotor Design
Some parameters based on the fundamental aerodynamic theories
are needed in order to receive more energy from the wind and
produce more power from the rotor. These parameters can be
expressed as follows [4]:
1. Radius of the rotor ( ) 2. Tip speed ratio of the rotor at
the design point ( )
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3. Number of blades ( ) 4. Design lift coefficient of the
airfoil ( ) 5. Angle of attack of the airfoil lift ( )
The first parameter, radius of the rotor, depends on the speed
of wind and the power expected from the turbine which can be
expressed at the design point as:
12 4.13
As we know , therefore the radius of the rotor can be defined
as:
4.14
where is the design power coefficient of the rotor, is the drive
train efficiency, is the generator efficiency and is the design
wind velocity [4].
Design tip speed ratio depends on the function of the turbine
which is applied. For instance, wind pump rotors need low tip speed
ratio due to the high starting torque. However, electricity
producing wind turbines require high tip speed ratio due to the
fast running rotor.
Number of blades in a rotor is directly related to the tip speed
ratio which means that we need lower blades for the higher tip
speed ratio and vice versa.
Figure 4.7 shows the number of blades based on the design tip
speed ratio in order to select the appropriate numbers of the
blades.
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Figure 4.7. Number of blades and design tip speed ratio
As it is mentioned before, the lift and drag coefficients are
the properties of an airfoil which can be found under wind tunnel
experiments. These coefficients may be available for some standard
airfoil sections at different angles of attack and can be used in
rotor design. In order to get more performance from the rotor, we
need to maximize the lift force and minimize the drag force by
reducing the angle of attack that can be obtained by plotting a
tangent to the curve of - as it is shown in figure 4.8.
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Figure 4.8. - relationship of an airfoil
If such data are not simply available for the selected airfoil,
the necessary information should be achieved through wind tunnel
experiments, figure 4.9.
Figure 4.9. A low speed wind tunnel
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4.1.5 Rotor Blades Material
The properties of the rotor blades materials depend strongly on
the blade dimensions, operating wind circumstances, and stresses
which arise from bending moments on the hub structure. In order to
construct the high size wind turbines, rotor blades are made from
glass-reinforced plastic (GRP), carbon fiber-reinforced plastic
(CFRP), steel, and aluminum [3]. On the other side, the production
efficiency and cost of construction for small wind turbines, which
can be categorized by the rotor diameter (smaller than 5 m), are
more important than weight, stiffness, and other design
requirements.
Foam, Gel coat, glass fibers, and epoxies are the most used
materials in the composite in order to build long blades with high
stiffness and lightweight characteristics. For instance, Fiberglass
offers high stiffness, flexural strength, and shear resistance
under extreme thermal and mechanical environments. Some designers
have considered high-performance resins such as epoxy in production
of rotor blades. Therefore, it is important to evaluate the
critical performance characteristics of resins which are viscosity,
exothermic properties, and other factors, in order to be sure that
the blade can be tolerated to the stresses and other causes.
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25
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26
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27
The active part of the protection system is the brake system
which is consisted of two independent systems: an aerodynamic brake
system and a mechanical brake system. An aerodynamic brake system
controls the blade tips which can be adjusted or the entire rotor
blade can be pitched. The mechanical brakes are usually used as a
backup system for the aerodynamic braking system in the wind
turbine [4]. They consist of brake calipers, brake discs and brake
pads.
The wind turbine generator transforms the mechanical energy of
the shaft into electric power. While the blades transfer the
kinetic energy of the wind into rotational energy in the
transmission system, the generator provides the next step in the
supply of energy from the wind turbine to the electrical grid.
Yaw mechanism lines up the plane of rotation to be vertical to
the direction of wind. The yaw mechanism is classified into passive
yaw and active yaw. The passive yaw is used for small wind turbines
and downwind turbines. The active yaw, the second type, is used in
most of the upwind wind turbines. This type of yaw mechanism uses
an electromechanical drive and a control system in order to control
and monitor the yaw in a wind turbine.
4.4 Tower
The tower of a wind turbine supports the nacelle and the rotor
and provides the safe and reliable operation of turbines under a
variety of wind conditions [6].
In order to capture more energy from the wind and generate more
power, the possible solution is using higher tower. Manufactures
prefer to produce taller towers due to utmost safety, optimum
performance and better design flexibility. On the other hand,
transportation, assembly and servicing of the components become
more difficult and costly when the height of the tower increases
[4].
The second design parameter of a tower is its stiffness.
Determining the first natural bending frequency in the right way is
an important task in the design [5]. This establishment helps
designer to choose the suitable materials for the tower in order to
achieve the required stiffness at the
-
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28
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29
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5.1 Aerodynamic loads
The aerodynamic loads are caused by airflow when it is passed
from the turbine blades and the tower, thus, the aerodynamic loads
can be separated into aerodynamic loads along the blades, described
in section 4.1.1.2 (Lift force and Drag force), and aerodynamic
drag force on tower which is defined as:
0.5 5.1
where is aerodynamic drag coefficient and A is projected area
vertical to the flow. Furthermore, in high wind speed situations,
when a wind turbine is stationary, the drag forces are the primary
consideration whereas the lift forces are more concerned when the
turbine is operating [1].
5.2 Gravity Loads
The gravity loads is an important source of loads that can be
imposed large fatigue stresses on the rotor and the tower. When the
dimension of wind turbine grows, the structure’s weight becomes the
main problem with respect to strength. The gravity forces are
simply given as:
5.2
Where is the mass of the i-th blade element and 9.82 . The
gravity on the tower equals to:
5.3
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5.3 Centrifugal Loads
The influence of inertial forces on blades’ mass which causes
moments to pitch the blades is called centrifugal loads. Due to low
rotation speed of the rotors in large wind turbines, centrifugal
forces are not very considerable [4]. On some rotors, however,
blades are flapped into the out-of-rotating-plane direction which
causes the cone angle between the blades and the rotational speeds.
This angle in some conditions can be reduced the blade-root bending
loads and in contrast, leads to an increase in the mean flap wise
bending. The centrifugal loads on the rotor equal to:
5.4
in which is the mass of the i-th blade element, is the radial
position of the i-th blade element in a discretisation of the blade
into n elements and is the angular rotor speed.
5.4 Gyroscopic Loads
The gyroscopic loads are caused by the rotation of the rotor
when it is yawed into the wind. A fast yawing rate is made a large
gyroscopic moments which reveal as pitching moments on the rotor
axis [4]. However, the yawing rates in horizontal wind turbines are
normally low due to using the active yaw mechanism, whereas the
gyroscopic forces in the wind turbines with passive yawing are the
significant problem.
The rotor is needed to also be yawed very quickly when wind
directions are changed rapidly during low wind speeds. Therefore,
rotor blades, under this condition, are faced to extraordinary
bending loads [6]. This is another reason that passive yaw
mechanism are applied in downwind rotor which are no longer being
built.
-
32
5.5 Wind Turbulence
The turbulence of the wind is the fluctuation of the wind speed
in short time scale which acts as a dynamic load in wind turbines.
Thus, wind turbine components can be influenced by fatigue loads,
particularly on the rotor blades, due to the large turbulence when
the speed of wind is significantly high. It is helpful to think of
the wind as comprise of a mean wind speed which fluctuates on a
time-scale of one or several hours. Wind speed naturally fluctuates
in all three directions, longitudinal, vertical and lateral
directions [6]. The turbulence model, however, is assumed only in
one direction, longitudinal, due to the difficult numerical
handling of two dimensional turbulence models and the influence of
longitudinal turbulence over the rotor-swept area.
The main parameter in turbulence is intensity which measures
rapid changes in wind speed over short intervals:
5.5
where is mean wind velocity is the standard deviation ration at
the same point and averaged over same period of time.
In general, the highest turbulence intensities occur at the
lowest wind speeds [6], but the lower limiting value at a given
location will depend on the specific land features and surface
conditions at the location.
5.6 Wind Shear
Wind shear is meteorological phenomenon which describes the
changes in wind speed as a function of height [6]. The velocity of
wind around the ground surface is theoretically considered to be
zero due to the frictional resistance of the airflow around the
ground. Thus, the rate of wind velocity increases with the height
which is an important factor in designing of wind energy plant.
Figure 5.2 displays the wind speed changes respect to height.
-
33
Figure 5.2. Wind flow in boundary layer
The power law is the most common method to describe the average
wind speed as a function of height above the ground which is
defined as [12]:
5.6
in which are wind speeds at heights , and is the wind shear
coefficient which depends on some factors, such as height, time and
locations. This coefficient is normally considered between
0.15-0.3., as shown in figure 5.3.
-
34
Figure 5.3. wind speed respect to height for different values of
shear, the
average wind speed is given 8 m/s at 50 m
-
6.
6.1
ThepartThisdiffefinitconnsolvelemmayall esolu
The
2
Theor
1 Finite E
e FEM is one otial differentias method appli
ferential equatite number ofnected to each
ved by defininment. These fuybe linear, quaelements are
ution for the en
Figure 6
e major steps in
1. Find the ssystem.
2. Convert th
ry
Element M
of the most poal equations wies a variationion over the mf sub
domainh other at the png approximatunctions shouladratic or
highknown then t
ntire region [2
6.1. Typical fin
n FEM are [13
strong form of
he strong form
35
Method (FE
owerful numerwhich are appenal problem whmodel domain.ns called
elepoints called nte interpolatiold be a complher order. Whethey
are place1].
nite element me
3]:
f the governin
m of the equatio
EM)
rical methodseared in enginehich involves a This domainments and
th
nodes. The subn or shape fulete set of polen the polynomed
together in
esh (two dimen
ng differential
on to the weak
for resolving eering probleman integral of is divided int
he elements b domains can unctions for ealynomials, whmial
functionsn order to find
nsional)
l equation of
k form.
the ms. the o a are be
ach ich
s of d a
the
-
36
3. Choose suitable interpolation (shape) functions. 4. Choose
the weight functions and set up the algebraic equations for
each element. 5. Obtain the global matrix system of the
equations through the
assembly of all elements. 6. Impose boundary conditions. 7.
Solve the system of algebraic equations. 8. Postprocess the
results.
6.2 Computational Fluid Dynamics (CFD)
CFD is a numerical method which can be used to predict fluid
flow, heat transfer and chemical reactions in complex systems. CFD
has been applied most widely in industrial and non-industrial
application areas due to less times and costs requirement in
designing models [10]. In order to analyze a fluid problem with
CFD, we need to obtain the mathematical equations which describe
the behavior of the fluid flow.
6.2.1 Governing equation
All fluid dynamics are based on three fundamental physical
principles: Mass conservation, Newton’s second law (Momentum) and
energy conservation.
6.2.1.1 Mass conservation The conservation of mass means that
the rate of mass flow into a fluid element (volume) equals to the
rate of increase of mass in the fluid element (volume) [10],
therefore for a compressible fluid:
ρ div 0 6.1
where is density of the fluid and is the velocity vector in
Cartesian coordinates.
-
37
And the density of an incompressible fluid, such as liquid, is
constant ( 0 , so:
div 0 0 6.2
where , are the velocity components of .
6.2.1.2 Newton's second law Newton's second law declares that
the rate of change of momentum equals to forces summation on the
fluid particles. The forces can be divided to surface forces as
separate terms and body forces as source term [10]. Then, the
momentum equations in three directions can be obtained by
considering the stresses in terms of the pressures on a control
volume. Therefore, the momentum equation in x, y and z components
equals to:
div 6.3a
div 6.3b
div 6.3c
where , are body forces (source term), for example the value of
body forces due to the gravity will be [10]: 0 ,0 . The stress
components are obtained by Navier-Stokes equations.
6.2.1.3 Energy equation The energy equation is obtained by the
first law of thermodynamics which describes the rate of change of
energy of a fluid particle is equal to the rate
-
38
of heat addition to the fluid particle plus the rate of work
done on the particle [10]. Hence, the energy equation equals
to:
div div div
6.4
where is the internal energy, is the temperature, is the thermal
conductivity, p is the pressure, u, v and w are the velocity
components of u and is a new source term which is a source of
energy and is a Mechanical (Kinetic) energy source.
Therefore, the equation of energy for compressible fluids will
be:
div div
6.5
where is the specific total enthalpy and is an enthalpy energy
source.
6.2.1.4 Navier-Stokes equations There still some unknown
variables, the viscous stress components , are remained in previous
equations. These values can be obtained by presenting the suitable
model which is represented as functions of the local rate of
deformation for most of the fluid flows. The local rate of
deformation is made of the linear deformation rate and the
volumetric deformation rate in
-
39
three-dimensional flows [10]. The Newton's law of viscosity for
compressible flows composed of two constant viscosities, dynamic
viscosity, , which is related to linear deformations and the second
viscosity, , which is related to the volumetric deformation.
Therefore, the six viscous stress components are constant and three
of them are variable. These components are explained as:
2 , 2 , 2
,
6.6
By substituting the equations 6.6 to equations 6.3a, b, c we
will reach to the Navier-Stokes equations:
div 6.7a
div 6.7b
div 6.7c
6.2.2 Finite Volume Method
Finite Volume Method (FVM) or Finite Control Volume Method is
the most popular discretization method in CFD. This method divides
the main domain into control volumes and then integrates the
equations over each control volume. The FVM method in some features
is similar to finite different method while the descritization form
is connected to the finite element method. The computational effort
of this method is greater than finite difference method and less
than the finite element method for a
-
similar accuravalue which (mass, momesecondly, the
Figure 6.2. T
The general c
where is a f
By integratiobecomes
acy [21]. In ahas some ad
entum, energycomplex geom
Typical finite v
onservation eq
fluid property
n of equation
divCV
40
addition, the Fdvantages, firy) remains cometries can be
volume grid tw
quation is equa
div
and Γ is the di
n 6.8 over a c
FVM is basedst the conseronserved at tmeshed.
wo dimensiona
al to:
Γ
iffusion coeffi
control volum
Γ
d on the cell arvation of quthe local scal
al (rectangular
icient.
me [10], the eq
average antities les and
r grid)
6.8
quation
6.9
-
41
By applying Gauss' divergence theorem, equation (6.9) can be
written as follow [10]:
.A
. Γ
6.10
The change rating term of (6.9) for the steady state problems is
equal to zero, therefore,
.A
. Γ 6.11
And for the transient problems, the equation will be [10]:
Δ
.A
Δ
. Γ Δ
Δ
6.12
6.2.3 Turbulence modeling
Turbulent flow is a type of fluid (gas or liquid) flow when the
velocity and other properties of the fluid fluctuate in all
directions. Using the Navier–Stokes equations for a turbulent flow
is extremely difficult due to the time-
-
42
dependent, nonlinear and three-dimensional equations. Hence, the
Reynolds Averaged Navier-Stokes Equation (RANS) is the most widely
used for calculating industrial flows [10]. The RANS can be
obtained from Navier–Stokes equations by considering the mean
properties for the flow such as mean velocities, mean pressures and
mean stresses etc., therefore the equations 6.7a, b, c become
[10]
div ′ ′ ′ ′ ′
6.13a
div
′ ′ ′ ′ ′ 6.13b
div ′ ′ ′ ′ ′
6.13c
The additional parts of equation on the mean velocity components
U, V and W are turbulent stresses which called Reynolds stresses.
where:
′ ; ′ ; ′ ; ′ ; ′
u, v, w are the velocity components of u ; U,V, W are the mean
velocity components of U; ′, ′, ′ are the fluctuating velocity
components of ′ and ′ are mean and fluctuating component of
pressure.
-
43
The Reynolds stresses could be obtained from mean rates of
deformation which is equal to [10]:
′ ′ 6.14
where is the turbulent viscosity which is determined by
different models.
6.2.3.1 The model The considered model for the free stream fluid
is the model which has one equation for the turbulent kinetic
energy, k, and one equation for the turbulent dissipation rate, .
Hence, the turbulence viscosity of this model can be obtained by
the below equation:
6.15
where is a dimensionless constant, k and are determined by the
following equations:
div 6.16
div 6.17
is the turbulence production and , , are constants and equal to
[10]:
1 ; 1.3 ; 1.44 ; 1.92
6.2.3.2 The model This model is suitable for calculating the
turbulence near the wall. The
model is based on model transport equations for the
turbulence
-
44
kinetic energy, k, and the specific dissipation rate, . These
values are derived from the equations below:
div ′ 6.18
div 6.19
, , , ′ are constants and equal to:
1 ; 2 ; 59 ; 0.075 ; ′ 0.09
Therefore, the turbulence viscosity of this model will be:
6.20
The advantage of this method is using the low-Reynolds number
near the wall and easier modeling which gives us more accurate and
more robust result but the disadvantage of this method is high
sensitivity to the free-stream conditions [25].
6.2.3.3 The Shear-Stress Transport (SST) model The SST model is
based on the model and has the same automatic wall treatment. This
model is mixing the best properties of model and model which means
around the near-wall region is using the
model and in free-stream flow is using the model in order to get
better results [25].
-
45
6.3 Fluid structure interaction
When the system is a coupled of fluid and solid structure then
it is called fluid structure interaction (FSI) which means that the
fluid effects on deformation of solid geometry and the deformed
geometry is changing the fluid variables, too. The FSI is an
example of a multiphysics problem which the fluid and solid have
interacted with each other. Two types of FSI have supported by
mechanical application in ANSYS, one way FSI and two ways FSI. The
result from CFD analysis is applied as a load to the mechanical
analysis and if the result has passed back to CFD then it is called
tow way FSI otherwise is called one way FSI [25].
The one way FSI allows computational fluid dynamics (CFD) and
finite element analysis (FEA) solvers to be run independently
whereas in two ways FSI, both solvers have to be run at the same
time because the results are transferred between CFD and FEA for
each step until overall equilibrium is reached among the Mechanical
application solution and ANSYS CFX solution. In this research, we
are considered the one-way FSI for our simulation.
-
46
7. Simulation
7.1 Geometry
The structural model contains the full geometry of wind turbine
which is tower, nacelle and rotor. The 3D model has been created in
ANSYS/DesignModeler based upon published information of 5MW wind
turbine from Repower [27], as shown in table below:
Table 7.1. 5MW wind turbine specifications
Rotor Nacelle Tower
Diameter 126 m Length 19 m Hub height 120 m
Blade length 61.5 m Width 6.8 m material Steel
Max. blade width 4.6 m Height 6 m weight 540 tone
Blade material GFRP with Epoxy Weight 316 tone Up diameter 5.5
m
Weight of each blade 18-19.5 tone Down diameter 6 m
Rotor weight 125 – 129.5 tone
Maximum rotation speed 12.1 rev/min
Figure 7.1 illustrates the final 3D structural model which has
been designed and the real model from Repower. In the next step,
the solid model has been inserted in a proper wind farm which has
been recommended by the manufacturer, as shown in figure 7.2.
-
6D
Figure 7.1. N
Figure 7
D (756 m)
47
Numerical and
7.2. Wind farm
real models
m model
4D (504 m)
1.5D (189m)
-
48
7.2 CFX
7.2.1 Mesh
The aim of CFX-mesh is producing high quality meshes which can
resolve boundary layer phenomena and fulfill severe quality
criteria [25]. CFX-Mesh makes meshes including tetrahedral, prisms,
and pyramids in standard 3D meshing model and also can be contained
hexahedra in the 2D meshing mode. In this project, tetrahedral mesh
has been chosen with advance size function in ANSYS due to the
complexity of model. This function can be effective for creating
high quality meshes around the solid walls. In addition, Mapped
face meshing has been used for the faces of the nacelle, rotor and
the tower in order to provide more uniform meshes. According to the
ANSYS help, different types of analyses have different meshing
requirements which mean that we should create finer mesh with slow
transition in CFD problems whereas coarser mesh with higher order
elements and faster transition should be used in mechanical
problems [25].
Figure 7.3 shows the final mesh that has been created in the CFX
part. The total number of mesh which has been used in the CFX part
equals to 2.5 million.
(a)
-
49
(b)
(c)
Figure 7.3. CFX mesh details (a) whole domain, (b) half of the
whole domain, and (c) rotor, nacelle and tower
7.2.2 Model set up
The next step after creating the appropriate and suitable meshes
for all the parts in CFX is specifying domains, boundary
conditions, type of analysis, interfaces, etc. In order to solve
the problem, it is necessary to create at least two types of
domains which are a stationary and a rotating. The nacelle and the
tower are considered inside the stationary domain and the rotor is
inserted in the rotating domain. Then, three interfaces have
been
-
defined betwchanges in ref
In order to roinstead of stechanging withthe analysis
significant pasmall enougheach domain discussed in th
Figure 7.4 rsimulation.
The next stepbelow:
Inlet According to is changing winput wind spassumed to be
Stationary dom
ween the statioference frames
otate the rotoady state analh time. Therefosection. It sh
arameter in thh to resolve th
is another fhe next part.
epresents the
Figu
is to define th
the wind sheawith the heightpeed in the ine air at 25 .
main
50
onary domain s.
r in ANSYS, lysis which mfore, total time hould be notede
transient sim
he problems afactor in the
domains wh
ure 7.4. Doma
he boundary co
ar principle, the. Thus, the equnlet boundary
and the rota
we should ueans that the vand time step
d that the sizmulations andappropriately.
transient ana
hich have bee
ains in CFX
onditions for t
e speed of winuation 5.5 is d
y layer. The t
ating domain
use transient avariables of fl should be def
ze of time sted must be conThe initial va
alysis which w
en supposed
the whole dom
nd is not constdefined and settype of fluid
Rotating dom
due to
analysis low are fined in ep is a sidered
alue for will be
in the
mains as
ant and t as the is also
main
-
OutTheexitpresturb
Figu
TurThehavemodchap
tlet e type of outleed and enteressure is also subine.
ure 7.5 shows
rbulence mode turbulence me been chosendel respect topter.
G
Outlet (openi
et has been coed through theupposed to be
the assumed b
el model for the n Shear Stress To the k-ε mo
Figure 7.5. B
Ground
ing)
51
onsidered opene boundary suzero due to un
boundary cond
stationary domTransport (SSodel which w
Boundary cond
ning class whurfaces. The vnbounded area
ditions in the si
main and the T) due to the a
was described
ditions in CFX
here fluid can value of relataround the wi
imulation.
rotating domadvantage of tin the previo
X
Inlet (Specif
Interface
be tive ind
ain this ous
fied velocity)
es
-
52
Initial conditions In order to solve the transient problems, we
have to specify the initial conditions for each domain since the
data describes the state at the simulation start time [25]. In
stationary domain initialization, the type of velocity has been
considered in Cartesian coordinate with the zero values, whereas
Cylindrical coordinate has been chosen with the same values for the
rotating domain. The relative pressure between inlet and outlet
boundary layers is also assumed to be zero in both domains.
According to the specification of the wind turbine, the angular
velocity of the rotating domain should be set at 12.1 which is the
maximum rotation speed of the rotor. Therefore, the rotor speed has
been fixed at the constant value in the software.
7.3 Structural
7.3.1 Mesh
In structural section, different types of mesh have been carried
out for all the parts. Hexahedron and tetrahedron are the suitable
meshes for the nacelle and tower. The appropriate mesh, however,
for the rotor is only tetrahedron due to the complexity of the
shape. Figure 7.6 shows the final meshes which have been created
for all the parts.
-
53
Figure 7.6. Different types of meshes for mechanical part
The number of elements and nodes for each type of mesh can be
seen in table below:
-
54
Table 7.2. Different meshes statics
Mesh Nodes Elements
Tetrahedrons 1434062 726347
Tetrahedrons + Hexahedrons 1128165 412554
The simulation has been done with the second type of mesh
(hexahedron and tetrahedron meshes).
7.3.2 Model set up
In this section, the boundaries and loads are defined for the
model in order to calculate the stresses and deflections in the
tower and the rotor. The significant feature in structural part is
importing the effective forces from the CFX into the mechanical.
Therefore, ANSYS is mapping the forces on each node in CFX into the
mechanical node which depends on some factors such as quality of
the mesh, element size, etc [25]. It should be noted that we should
check the percentage of mapping and the value of forces after
importing the loads in order to be sure that all the forces are
properly mapped. Figure 7.7 illustrates the imported loads on the
rotor, nacelle and the tower from CFX into the Mechanical.
-
55
Figure 7.7. Imported loads on the tower, nacelle and the
rotor
-
56
8. Results
The simulation has been carried out with transient analysis for
80 seconds with time step size of 0.1. Figure 8.1 represents the
different snapshots of the wind velocity at 80 second in the
stationary domain. It should be mentioned that the rotating domain
has not been considered in these figures due to high velocity
changes around the rotor. As can be seen from the figures, the
speed of the wind has been changed around the tower and the nacelle
due to the rotation of the rotor.
(a)
-
57
(b)
Figure 8.1. Velocity of the wind in the stationary domain in
different snapshots at 80 sec, (a) in XY plane (left view), and (b)
in XZ & XY plane
When the energy of the wind is extracted by a wind turbine, then
the air leaves the turbine with less speed, less energy and higher
turbulence level, which is called the wake of a wind turbine.
Another wind turbine operating in this wake will therefore produce
less energy and tolerate greater structural loading than a turbine
operating in the free stream. Figure 8.2 shows the shape of the
wake turbulence behind the wind turbine when the air passes through
the turbine.
-
58
(a)
(b)
Figure 8.2. Wake Turbulence behind the wind turbine, (a) Front
view, and (b) Isometric view
-
59
In order to import the loads from the CFX into the Mechanical,
first we should obtain the influence of wind forces on the nacelle,
tower and the rotor. In figure 8.3, the value of wind forces on the
rotor has been caculated in all directions. As can be seen from the
figure, the maximum force on the rotor is in direction of the wind
which is increased sharply and then gradually reach to the maximum
value. On the other hand, the forces values in other directions are
almost equal to zero. Figure 8.4 shows the impact of wind forces on
the nacelle and the tower which is not constant and changing
periodically due to influence of the turbulence. These changes in
scale of turbulence increase the structural vibrations of the wind
turbine, which cause increased fatigue loads.
Figure 8.3. Wind forces on the rotor
‐1.0E+05
0.0E+00
1.0E+05
2.0E+05
3.0E+05
4.0E+05
5.0E+05
0 10 20 30 40 50 60 70 80
Force [N]
Time [s]
Force (X) Force(Y) Force (Z)
-
60
(a)
(b)
Figure 8.4. Wind forces on the (a) nacelle and the (b) tower
‐4.0E+03
‐3.0E+03
‐2.0E+03
‐1.0E+03
0.0E+00
1.0E+03
2.0E+03
3.0E+03
0 20 40 60 80
Force [N]
Time [s]
Force (X) Force (Y) Force (Z)
‐5.0E+04
‐4.0E+04
‐3.0E+04
‐2.0E+04
‐1.0E+04
0.0E+00
1.0E+04
2.0E+04
3.0E+04
4.0E+04
5.0E+04
0 20 40 60 80Force [N]
Time [s]
Force (X) Force (Y) Force (Z)
-
61
The stresses and deflections in each part can be estimated after
importing the loads from the CFX into the Mechanical part. Figure
8.5 and 8.6 illustrate the stresses and deflections in the tower
and the rotor, respectively. As it can be seen in these figures,
the maximum stress in the tower is located at the lowest point of
the tower.
Figure 8.5. Stresses in the tower and the rotor
(scale factor=62)
-
62
Figure 8.6. Deformations in the tower and the rotor
(scale factor=62)
And finally, the influence of gravity forces on all the parts in
structural has been investigated. As we can see from the figure
8.7, the stresses in the tower and the rotor are siginifantly
higher than the case which is turbulence
-
63
loads effect on these parts. Therefore, the gravity forces are
very important loads and should be considered in designing of the
large wind turbines.
Figure 8.7. Gravity loads on tower and rotor (logarithm scale
with a scale
factor of 82)
-
64
9. Conclusion
The purpose of this research has been to investigate the effect
of turbulence and gravity loads on the tower and the rotor of a 5MW
wind turbine in order to calculate the stresses and deflections in
these parts.
For this goal, a full 3D-model of a 5MW onshore wind turbine was
simulated by using the commercial software ANSYS. The simulation
was set with fairly realistic domains and boundaries which had
considerable influences on the outcomes.
The results represented that the turbulence after the rotor was
influenced on the wind turbine as dynamic loads which cause
increased fatigue loads on the structural parts. The fatigue loads
decrease the lifetime of components and might be brought them to
failure. In addition, the gravitational load of each part must be
taken into account in designing of a wind turbine. As it was shown
in the result section, the gravitational loads were higher than
turbulence loads in the large wind turbine and both loads with
together become dominant factor for the fatigue load in each
component in wind turbines.
Wind turbines are generally grouped together in wind farms and
some of them operate partly or fully in the wake turbulence of
upstream turbines. These downstream turbines are faced to the wind
with higher turbulence and less energy which increases the fatigue
loading in the components. Therefore, the influences of turbulence
loads in downstream wind turbines are higher than upstream wind
turbines. However, when the downstream turbines are far enough from
the upstream turbines, the wake wind speed will recover to the free
stream value and then the effect of turbulence loads will be normal
and not so high. The distances between wind turbines are thus have
an important factor in the value of turbulence loads on the
turbines in a wind farm.
-
65
10. Future Works
This research tried to investigate the effect of two important
types of loads on an enormous wind turbine. Other explorations can
be executed with this 3D-model in the future:
Implementing different types of turbulence models in simulation
and comparing the results.
Calculating the fatigue loads on the wind turbine components.
Modifying the blade shape and calculating the aerodynamic loads
in
the wind turbine.
Calculating the effect of turbulences and wind forces on the
components with extreme wind speed condition which is exceeded only
once within a period of 50 years.
Investigating the load effects of upstream on downstream wind
turbines in a wind farm.
Study of the turbulent wake behind a wind turbine.
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66
11. References
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ENERGY EXPLAINED: Theory, Design and Application (2nd Edition),
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2. A.R. Jha, (2008), Wind Turbine Technology, CRC Press. 3.
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4. Sathyajith Mathew, (2006), Wind Energy: Fundamentals,
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5. Tony Burton, David Sharpe, Nick Jenkins, Ervin Bossanyi,
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10. H. K. VERSTEEG and W. MALALASEKERA, (1995), An introduction
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12. Pramod Jain, (2010), Wind Energy Engineering, McGraw-Hill
13. Broman, Göran, (2003), Computational Engineering, Bleking
Institute
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14. Olimpo Anaya-Lara, Nick Jenkins, Janaka Ekanayake, Phill
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15. European Wind Energy Association (EWEA), (2009), Wind Energy
The Facts: A Guide to the Technology, Economics and Future of Wind
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67
16. Thomas Ackermann , (2005), Wind Power in Power Systems, John
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17. Mathew Sathyajith, Geeta Susan Philip, (2011), Advances in
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18. Erich Hau, (2006), Wind Turbines: Fundamentals Technologies
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School of Engineering, Department of Mechanical Engineering
Blekinge Institute of Technology SE-371 79 Karlskrona, SWEDEN
Telephone: E-mail:
+46 455-38 50 00 [email protected]