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DESIGN, BULIDING ANDTESTING A VERTICAL

AXIS WIND TURBINE

by

Tan Chee Kwang

A thesis submitted in partial fulfillment ofthe requirements for the degree of

Bachelor of Mechanical Engineering

University of Newcastle

2012

Approved by ___________________________________________________Project Supervisory Committee

__________________________________________________

__________________________________________________

__________________________________________________

Program Authorizedto Offer Degree _________________________________________________

Date 09-APR-2012

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UNIVERSITY OF NEWCASTLE

ABSTRACT

DESIGN AND DEVELOPMENT OF VERTICAL AXIS WIND TURBINE

by Tan Chee Kwang

Project Supervisory Committee: Dr William Yeung

This report is continue from the previous report, which list out the objective and

introduction of the project.

Previously the report mainly focuses on the objective of the project and research

on various vertical axis wind turbine.

The first phase of the Part B, will be study on the aerodynamics of the vertical

axis wind turbine and how does the design parameter developed from it. After

acquire the parameter, the design of the wind turbine is proceed on. It consist of

mechanical design and fatigue analysis using computational FEA.

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ACKNOWLEDGMENTS

This project was assisted and guided by Dr. William Yeung and some guidance by

Dr. Arezki. Appreciation to them for provide useful information and inject some

idea into the project, to make the project run smoothly.

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TABLE OF CONTENTS

List of Figures ....................................................................................................................... ii

List of Tables ........................................................................................................................2Chapter II: Literature Review ............................................................................................3

2.1 Introduction ....................................................................................................32.2 Aerodynamics of aerofoil ..............................................................................42.3 Geometry of Aerofoil...22.4 Bernoullis principle .......................................................................................52.5 Angle of attack vs Coefficient of Lift/Drag .............................................62.6 Single stream tube model ..............................................................................92.7 Aerodyanmics of Vertical Axis Wind Turbine.......112.8 Design Parameter of Vertical Axis Wind Turbine.14

Chapter III: Wind energy review.....15

3.1 Introduction ..153.2 Type of VAWT Selection.153.3 Scaling of VAWT....163.4 Input of Design Parameter..163.5 Shaft Design....183.6 Shaft Stress and Fatigue Analysis.19

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Chapter 2: Literature Review

2.1Introduction

To successfully design the vertical axis wind turbine (VAWT), it needs a basic understanding of the

aerodynamics between the blades and the wind. The performance of the VAWT is based on howefficient it can extract the wind energy.

The fundamental principle of the extraction of wind energy is based on two force acting on the wind

turbine blade which is: lift force and drag force. These two forces determine the performance rating ofthe wind turbine, and the shape and size of the blade also influence how much force will acting on theblade.

Hence the relation between blade and the two forces is an important parameter, to understand better how

it will develop a steady state aerodynamics equation to predict the problem and performance of the windturbine.

So firstly is to understand the basic fundamental of the lift and drag force, then the aerodynamics of theVAWT.

2.2Geometry of aerofoil

In fig 2.1, show the geometry of aerofoil. It basically have following key feature:

Theleading edgeis the point at the front of the aerofoil that has maximum curvature;

Thetrailing edgeis the point of maximum curvature at the rear of the aerofoil;

The chord length, or simply chord, c, is the length of the chord line and is the

characteristic dimension of the aerofoil;

Thechord lineis a straight line between the leading and trailing edges of the aerofoil.

http://en.wikipedia.org/wiki/Leading_edgehttp://en.wikipedia.org/wiki/Leading_edgehttp://en.wikipedia.org/wiki/Leading_edgehttp://en.wikipedia.org/wiki/Trailing_edgehttp://en.wikipedia.org/wiki/Trailing_edgehttp://en.wikipedia.org/wiki/Trailing_edgehttp://en.wikipedia.org/wiki/Chord_%28aircraft%29http://en.wikipedia.org/wiki/Chord_%28aircraft%29http://en.wikipedia.org/wiki/Chord_%28aircraft%29http://en.wikipedia.org/wiki/Chord_%28aircraft%29http://en.wikipedia.org/wiki/Trailing_edgehttp://en.wikipedia.org/wiki/Leading_edge

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2.3Aerodynamics of aerofoil

In aerodynamics, it is a study of force and moment acting on an object when a motion of air flowsthrough it. It classified into two categories which is external flow and internal flow. In this chapter, willbe focus mainly on external flow around an object. In an external flow, the object surrounded by motionof air can be varies. But the aerofoil will be the only object that will be subjected to discuss.

An aerofoil is a shape of wings or blade, when it moved through a fluid a aerodynamics force willproduce. This aerodynamics force which is perpendicular to the motion of the fluid is classified into twopart which is lift force and drag force. How this two force produce, in the next point a series ofillustration and explanation will show how the aerofoil form this two important force that produce thepower in wind turbine.

In Fig 3.1 it show an air flow pass through a aerofoil. The stream line is a path line of the mass airparticle moving on the flow. The curvature of the stream line is caused by the shape of the aerofoil,

which force the stream line to curve around the surface of the geometry. And this curvature is a pressure

gradient of fluid act around the aerofoil, which can describe as a mathematical term,

=2

.

Where is the wind speed and is the curvature of the stream line. This pressure gradient act as acentripetal force of the air particle at the air atmosphere. When the air particle flow pass the aerofoil, thepressure gradient occur at leading edge of the aerofoil which cause a pressure difference. This happen

due to the air particle is separate into upper part and lower part at the leading edge. As the distanceacross the curved top surface is longer than the bottom surface. The air flow faster at the top surface than

Fig 2.2 Air flow pass through a air flow

Fig 2.3 High pressure and low pressure occur at the

leading edge of aerofoil

Low pressure

High pressure

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the bottom surface in order the two side air particle to meet at the trailing edge at the same time. Theincrease velocity of the air created low pressure region at the upper surface, at the lower surface whichhad a lower velocity had higher pressure. Thus cause a pressure difference around the aerofoil. Thisdifference is stated by Bernoullis principle. Fig 3.2 explain the process.

2.4

Bernoullis principle

In fluid dynamics, Bernoullis principle stated that in a inviscid flow of the fluid, an increase speed ofthe fluid will cause a decrease of pressure. Thus the principle explains why there is a pressure differenceoccurs around the aerofoil.

As the pressure at the lower surface is greater than the upper surface, the air particle is tend to move

from high pressure to low pressure. This motion produce a lift force from the air particles. When thespeed of the air particles flow across the upper surface increase further, the lift force exceed the weightof the aerofoil and push it upward. Fig 3.3 illustrate the motion of the air particle.

In order to maintain the constant speed, a propulsion force need to balance the another force which isdrag force. Thus all the above force acting on the aerofoil create a force diagram on fig 3.4 which shown

below.

Where L is define as lift force, D is drag force, and N and A is define as normal force and axial force

which is not required in this chapter. The is define as angle of attack which will explain later how doesit affect the motion and force acting on the aerofoil.

Low pressure

High pressure

Fig 2.4 Bernoullis principle of motion of air particle

Fig 3.5 Force diagram of the aerofoil

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From the force diagram, the force of lift and drag is defined as:

=

1

22

(2-1)

=1

2

2 (2-2)

Where is lift coefficient, is drag coefficient, is air density, is the wind speed and is thechord length of the aerofoil.

The equation above indicates the amount of the lift/drag force:

Chord length of aerofoil

This related to the shape and surface of the aerofoil. A symmetrical aerofoil which has

no camber has shorter chord length then an unsymmetrical aerofoil. A aerofoil with nocamber has rougher surface which create turbulence and decrease lift force and increase

drag force.

Wind speed

Increase of wind speed will also increase the lift force, but in contrast the drag force

also increases as while.

Lift/Drag coefficient

The coefficient is co-related to the angle of attack, which the valve is collected during

the test. When the angle of attack increase the lift force also increase. But when theangle of attack increase too great, the turbulence will occur at the aerofoil and decrease

the lift force.

Air density

Density of the air plays an important role to the lift force of the aerofoil. The air near to

the earth surface is much more dense then the air at a higher altitude. Hence there will

be more lift force acting on the aerofoil. When the aerofoil at a higher altitude, the lift

force will also decrease.

2.5Angle of attack VS Lift/Drag coefficient

When the angle of attack reached a certain angle, stall occur at the aerofoil and separation on the

upper surface take place. This cause a wake to form at the upper surface which reduce lift force andincrease drag force. This explain in fig 2.6.

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An example of the lift/drag coefficient vs angle of attack relationship shown in fig 3.6 and fig

3.7 had tabulate by Sandia National Labs, which they use NACA 0015 aerofoil as an

experiment object. The result had shown that it fulfill the above explanation that lift force

decrease when angle of attack reached certain angles.

Fig 2.6 Stall and separation occur at aerofoil at the peak of

the lift coefficient

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This had summaries well on the aerodynamics of the aerofoil. As it apply to the vertical axis

wind turbine, the lift force will cause the aerofoil move in circular motion instead of moving

forward. Since the aerofoils had fixed to the rotor shaft of the turbine. A simple model which is

calculate the power coefficient and various parameter will discuss in the next points.

Fig 2.7 Coefficient of lift vs angle of attack

Fig 2.8 Coefficient of drag vs angle of attack

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2.6Single Stream tube model

The performance of the wind turbine can be determine by a simple model which created by

Betz (1926), it generally used to determine the power of an idea turbine and the thrust force

acting on the turbine. This model is based on the linear momentum principle to predict the

ship propellers performance.

This model assumes that the control volume boundaries surface is a stream tube and the

turbine is a actuator disk which create a discontinuity of the pressure in the stream tube.

In fig 3.8, it show example of the single stream tube model.

This model has following assumption [1]:

Homogeneous, incompressible, steady state fluid flow;

No frictional drag;

An infinite number of blade;

Uniform thrust over the disk or rotor area;

An non-rotating wake;

The static pressure far upstream and far downstream of the rotor is equal to the

undisturbed ambient static pressure;

Applying the conservation of linear momentum to the control volume enclosing the whole system, itis possible to find the net force on the contents of the control volume. That force is equal and oppositeto the thrust, T, which is the force of the wind on the wind turbine. From the conservation of linearmomentum for a one-dimensional, incompressible, time-invariant flow, the thrust is equal andopposite to the change in momentum of air stream:

4411 )()( AUUAUUT = (2-3)

where is the air density,A is the cross sectional area, V is the air velocity and the subscripts indicate

values at numbered cross sections in Fig 3.9 .For steady-state flow, mAUAU = 41 )()( , where

m is the mass flow rate. Therefore:

)( 41 UUmT = (2-4)

Fig 2.9 Single stream tube model [1]

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The thrust is positive so the velocity behind the rotor, U4, is less than the free stream velocity, U1. Nowork is done on either side of the turbine rotor. Thus the Bernoulli function can be used in the twocontrol volumes on either side of the actuator disk. In the stream tube upstream of the disk,

2

22

2

11

2

1

2

1pvppvp +=+

(2-5)

where it is assumed that the far upstream and far down-stream pressures are equal (p1=p4) and that thevelocity across the disk remains the same (U2= U3). The thrust can also be expressed as the net sum ofthe forces on each side of the actuator disc as:

)( 322 PPAT = (2-6)

Solving for )( 32 pp using Equations (3) and (4) and substituting into (5), it is possible to obtain:

)(21 24212 UUAT =

(2-7)

Equating the thrust values from (2) and (6) and recognizing that the mass flow rate isA2V2,

2

412

UUU

+=

(2-8)

Thus, the wind velocity at the rotor plane, using this simple model, is the average of the upstream and

down-stream wind speeds. If one defines the axial induction factor a, as the fractional decrease inwind velocity between the free stream and the rotor plane, then

1

21

U

UUa

=

(2-9)

)1(12 aUU = (2-10)

)21(14 aUU = (2-11)

From (6), (9) and (10), the axial thrust on the disk is:

[ ])1(42

1 21

aaAUT = (2-12)

The thrust on a wind turbine can be characterized by a non-dimensional thrust coefficient as:

)1(4

2

1 2aa

ForceDynamics

ForceThrust

AU

TCT ===

(2-13)

The power, P, is equal to the thrust times the velocity at the discs:

))((

2

1)(

2

14141222

2

4

2

12 UUUUUAUUUAP +==

(2-14)

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Substituting for U2and U4from equation (2) and (6) gives:

( )[ ]232 142

1aaUAP =

(2-15)

The power on a wind turbine can be characterized by a non-dimensional power coefficient as:

)1(4

2

1 3aa

PowerWind

PowerRotor

AU

PCP ===

(2-16)

The maximum CPis then determined by the derivative of the power coefficient with respect to a and

setting equal to zero yielding3

1=a . Thus,

593.0

27

16max, ==PC

(2-17)

For this case, the flow through the disc corresponds to a stream tube with an upstream cross-sectional

area of 2=3 the disc area that expands to twice the disc area downstream. This result indicates that, ifan ideal rotor were designed and operated such that the wind speeds at the rotor were 2=3 of the freestream wind speed, then it would be operating at the point of maximum power production.

Furthermore, given the basic laws of physics, this is the maximum power possible.

The Betz limit, CP,max= 16/27, is the maximum theoretically possible rotor power coefficient. Inpractice, three effects lead to a decrease in the maximum achievable power coefficient:

rotation of the wake behind the rotor;

finite number of blades and associated tip losses;

non-zero aerodynamic drag

2.7Aerodynamics of Vertical Axis Wind Turbine

In VAWT, the analysis of the stream tube model has been a established technique to predict theperformance of the VAWT. Although it can be complex as the flow velocity is not constant betweenupstream and downstream.

An illustration of the VAWT of the top view is shown below. In this diagram, the wind flow from up todown, and the turbine is rotating in counter-clockwise direction. As can be seen, a component due torotation is tangential to the circle of rotation, and thus parallel to the chord line of the aerofoil. Onecomponent of the wind also acts tangentially. Another wind component is normal to the circle, and so

perpendicular to the aerofoil. An induction factor, a , accounts for the deceleration in the wind as itpasses through the rotor.

The relative velocity , RV can be obtain from the cordial velocity component and the normal velocity

component by Pythagoras Theorem as follows:

( ) ( )22

cossin RVVV aaR ++= (2-18)

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whereaV is the axial induction flow( ( )aV 1 ) through the rotor, is the rotational velocity,Ris

the radius of the turbine, is the angle of attack, and is the azimuth angle.

Normalizing the relative velocity by using free stream velocity, V can obtain as follow,

22

cossin

++

=

RV

V

V

V

V

V aaR

(2-19)

Referring to the previous point where aV can be express as ( )aV 1 , the expression can be as follow,

( )( ) ( )( )22 cos1sin1 ++=

aa

V

VR

(2-20)

where is the tip-speed ratio of the wind turbine.

The angle of attack can be obtain as follow,

RV

V

a

a

+=

cos

sintan

(2-21)

by non-dimensionalizing the equation,

Fig 2.10 Aerodynamics of VAWT [2]

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+

=

V

R

V

V

V

V

a

a

cos

sin

tan

(2-22)

( )( )

+

=

cos1

sin1tan 1

a

a

(2-23)

The normal and tangential coefficient can be expressed as follow,

sincosDLn

CCC += (2-24)

cossin DLt CCC = (2-25)

where LC is the lift coefficient and, DC is the drag coefficient.

The torque on one single blade can be express as,

( )( ) cossin2

1 2DLR CChcRVT =

(2-26)

where h is height of the blade and c is the chord length of the blade.

The power produced by the rotor is found, as usual, from the product of the average torque and therotational speed. The torque varies with angular position, so the expression for power is:

=

2

02

1QdP

(2-27)

where Q is the total torque of turbine inBblade, that express as,

BTQ= (2-28)

Hence the average power, Pover one revolution can be expressed as,

( )

dCCVBcRhP DLR cossin

2

1

2

2

0

2 = (2-29)

Hence the power coefficient over the wind pass through the projected area of the turbine in 2Rh isdefine as,

PowerWind

PowerRotor

RhV

PCP

2

2

1 2==

(2-30)

dC

CCVV

RBcC

L

DL

RP

=

tan1sin

4

2

0

2

(2-31)

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2.8Design Parameter of Vertical Axis Wind Turbine

From the above power coefficient, the design parameter that affect the performance of the VAWT isdefined which is:

Rotor Solidity

The rotor solidity,R

Bc

2= is defined as the developed surface area of all blade

divided by the swept area and represent as one of the key parameter. For minimum cost,

the solidity should be keep as low as possible.

For maximum capture of the wind energy, the blade chord should be varying from

minimum from the mid-rotor to maximum at the ground.

Tip-Speed Ratio

The tip-speed ratio,

=V

R is defined as speed factor that controlled by the wind

regime, rotor solidity and power rating. It is possible to extract more energy by reduce

the blade area and increase the rotor speed. But this will cause the blade cannot

withstand the aerodynamics force and inertia load.

Aerodynamics Force and Angle of Attack

The aerodynamics force which is lift coefficient,LC , drag coefficient, DC , and angle of

attack, . All this factor is related to the shape and size of the blade and how does

position at the turbine.

Rotor Aspect Ratio

This ratio is defined by the ratio of height to diameter of the turbine. If the aspect ratio

is increased, the rotor speed also increased to maintain the same relative wind speed and

tip-speed ratio.

The optimum aspect ratio is varying between 1.3 to 1.5, with a few exception.

Above factor conclude the important design parameter to proceed on to the prototype design.

Next chapter will be discussing on the prototype design phase.

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Chapter 3: Mechanical Design And Selection3.1Introduction

After acquire the design parameter, the design of the prototype will based on this factors.

Firstly select what type of VAWT is the most priority in this phase, as it will determine what

type of blade will using.

Next will be scaling the size of the turbine, which will be one of the priorities in the design.

Based on the size selected, the parameter can be input in prototype design. Hence, it can

conclude and finalize the wind turbine design.

3.2Type of VAWT Selection

On the previous report, it mention on various type of VAWT. Considering the simplicity and

cost factor, the Lenz II wind turbine will be the best choice among all.

This VAWT is the easiest to fabricate among various type of wind turbine. Especially theblade, it can easily make without any complicated process compare to NACA type aerofoil

which required CNC machining. All this process required a lot of funds to injected to the

project, which will be over the budget that given to this project.

Hence, the blade design needs to be as simple as possible.

Fig 3.1 Lenz II Wind Turbine [3]

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3.3Scaling of VAWT

Next will be scaling of the wind turbine which decides the size of the turbine and blades. The

size of the turbine is based on the wind tunnel open section size. After measured the open

section of the wind tunnel, it is measure at 0.5m x 0.5m.

With this dimension form the wind tunnel, the size of the turbine can be finalize.

3.4Input of Design Parameter

With all the information above had acquired, it can input into the design parameter and set the

specification of the turbine.

Sweep Area and Height of the Turbine

Firstly is the sweep diameter and height of the turbine, it based on the measurement of

the wind tunnel open section. Hence the diameter will be turbine will 0.5m wide and theheight will be 0.5m. The area will be 0.25m2.

Blade Size and Properties

The chord length and width of the blade will be according to the formula that given in

Lenz blade website which is,

m

D

nceCircumfereChordWing

m

DiameterSweepWidthWing

141.0

09.0)5.0(

09.0

09.0

07.0

14.05.0

14.0

=

=

=

=

=

=

=

But for the purpose of convenience, the dimension is modified for fabricator to easily

process the fabrication. Hence the blade width will be 0.75m and chord length will be

0.170m. Below illustrate the dimension of the blade.

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Rotor Solidity and Number of Blade

Since the chord length and the sweep diameter had acquired in previous point, the

number of blade will be next factor need to deal with. Generally the VAWT is using

three blades for among all the turbine in the commercial market. But for purpose of

increase the torque of the turbine, the number of blades will be using 4.

Hence the rotor solidity can be calculate as follow,

43.0

25.02

17.04

2

=

=

=

R

Bc

The above value can be considered as low solidity.

Tip-Speed Ratio

The tip-speed ratio consists of rotor speed and wind speed generated by the wind

tunnel. But currently the rotor speed is unknown, hence it need to estimate a value. To

maximize the rotor speed that turbine can be withstand, 1800 rpm or 188.5 rad/s will be

the estimated speed. The maximum wind speed that a wind tunnel can produce will be

20 m/s.

The above value will tabulate the tip-speed ratio as follow,

36.2

20

25.05.188

=

=

=V

R

Rotor Aspect Ratio

Since the height and the sweep diameter had been defined, the rotor aspect ratio can be

tabulate as follow:

1

25.02

5.0

2

=

=

=R

hRatioAspectRotor

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3.5Shaft Design

The shaft of the turbine is one of the most important elements in the wind turbine. It is responsible forthe wind turbine structure and transmits the power to the energy converter. To select the suitable size forthe turbine that can withstand the load of the blade and can fit into the commercial bearing in the market,the size will be 7/8 UNC or 22.225mm diameter.

The material used on the shaft will be mild steel as it will be cheaper than and as strong as stainlesssteel. As the major factor for design the shaft had defined, the overall shaft design is illustrated belowwith properties table:

Material Mild Steel ASTM A36

Density of Material 7848 kg/m3

Mass 3.92 kg

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3.6Shaft Stress and Fatigue Calculation

The fatigue analysis general will be using von mises theorem, as it is the most practical fatigue theoremto use among the industry. But for the simplicity of the process, the calculation will be based on thecomputational FEA. The FEA software will be using Pro/Engineer Mechanica, this software will bebased on von mises criterion to tabulate the result.

Before starting of the FEA, it needs the force acting on the shaft which is the load of the blades. Thematerial of the blade will be using aluminium, which the mass of each blade is 965g. After acquire theforce, the input of the force diagram and result is illustrated below,

From the above result, it show that the maximum stress occur on the shaft is 1.814 MPa, which is lowerthan the yield strength of the mild steel, 250MPa. Hence is indicate that the shaft does not failure occur

when it is in static position.

FF

FF

F F

F F

Gravity Force

MaximumStress

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REFERENCES

[1] J.G.McGowon Wind Energy Explain: Theory,Design, and Application . Wiley (2009)

[2] Ion Paraschivoiu. Wind Turbine Design With Emphasis on Darrieus Concept. Pressesinternationales Polytechnique, 2002

[3] http://www.windstuffnow.com/main/vawt.htm