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

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

2

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

4

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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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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30

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.

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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.

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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

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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

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onditions for t

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y layer. The t

ating domain

use transient avariables of fl should be def

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alysis which w

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ure 7.5 shows

rbulence mod

e 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

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ditions in the si

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imulation.

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X

Inlet (Specif

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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.

66

11. References

1. J. F. Manwell, J. G. McGowan, A. L. Rogers, (1993), WIND ENERGY EXPLAINED: Theory, Design and Application (2nd Edition), John Wiley & Sons Ltd.

2. A.R. Jha, (2008), Wind Turbine Technology, CRC Press.

3. Martin O. L. Hansen, (2008), Aerodynamics of Wind Turbines (2nd Edition), Earthscan.

4. Sathyajith Mathew, (2006), Wind Energy: Fundamentals, Resource Analysis and Economics, Springer.

5. Tony Burton, David Sharpe, Nick Jenkins, Ervin Bossanyi, (2001), WIND ENERGY Handbook, JOHN WILEY & SONS Ltd.

6. Wei Tong, (2010), Wind Power Generation and Wind Turbine Design, WIT Press.

7. Jashua Earnest, Tore Wizelius, (2011), Wind power plants and project development, PHI Learning Pvt. Ltd.

8. Martin O. L. Hansen, (2008), Aerodynamics of Wind Turbines (2nd Edition), Earthscan.

9. DNV/Risø, (2002), Guidelines for Design of Wind Turbines (2nd Edition), Det Norske Veritas.

10. H. K. VERSTEEG and W. MALALASEKERA, (1995), An introduction to computational fluid dynamics, Longman Group Ltd.

11. Tore Wizelius, (2007), Developing wind power projects: theory and practice, Earthscan.

12. Pramod Jain, (2010), Wind Energy Engineering, McGraw-Hill

13. Broman, Göran, (2003), Computational Engineering, Bleking Institute of Technology.

14. Olimpo Anaya-Lara, Nick Jenkins, Janaka Ekanayake, Phill Cartwright, Mike Hughes, (2009), Wind Energy Generation: Modelling and Control, John Wiley & Sons, Ltd.;

15. European Wind Energy Association (EWEA), (2009), Wind Energy The Facts: A Guide to the Technology, Economics and Future of Wind Power, Earthscan.

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16. Thomas Ackermann , (2005), Wind Power in Power Systems, John Wiley & Sons, Ltd.

17. Mathew Sathyajith, Geeta Susan Philip, (2011), Advances in Wind Energy Conversion Technology, Springer.

18. Erich Hau, (2006), Wind Turbines: Fundamentals Technologies Application Economics(2nd Edition), Springer.

19. A. Rodríguez T., C.E. Carcangiu, I. Pineda, T. Fischer, B. Kuhnle, M. Scheu and M. Martin, (2011), Wind Turbine Structural Damping Control for Tower Load Reduction.

20. Vivek V. Ranade, (2002), Computational Flow Modeling for Chemical Reactor Engineering, ACADEMIC PRESS.

21. Alik Ismail-Zadeh, Paul J. Tackley, (2010), Computational Methods for Geodynamics, CAMBRIDGE UNIVERSITY PRESS.

22. Titus Petrila, Damian Trif, (2004), Basics of fluid mechanics and introduction to computational fluid dynamics, Springer.

23. Ion Paraschivoiu, (2002), Wind turbine design, Polytechnique.

24. Anastasis C. Polycarpou, (2006), Introduction to the finite element method in electromagnetic, Morgan & Claypool Publishers.

25. ANSYS Help; 2010

26. J. Jonkman, S. Butterfield, W. Musial, and G. Scott, (2009), Definition of a 5-MW Reference Wind Turbine for Offshore System Development.

27. Timo Siebels, (May 2007), REpower Systems AG.

28. http://www.repower.de/

29. http://www.house-energy.com/

School of Engineering, Department of Mechanical Engineering Blekinge Institute of Technology SE-371 79 Karlskrona, SWEDEN

Telephone: E-mail:

+46 455-38 50 00 info@bth.se