Vertical Axis Wind Turbine

MECH 4010 Design Project

Vertical Axis Wind Turbine

Group 2

Jon DeCoste Denise McKay Brian Robinson Shaun Whitehead Stephen Wright

Supervisors Dr. Murat Koksal Dr. Larry Hughes

Client

Department of Mechanical Engineering Dalhousie University

December 5, 2005

ii

EXECUTIVE SUMMARY

With the recent surge in fossil fuels prices, demands for cleaner energy sources, and

government funding incentives, wind turbines have become a viable technology for

power generation. Currently, horizontal axis wind turbines (HAWT) dominate the wind

energy market due to their large size and high power generation characteristics. However,

vertical axis wind turbines (VAWT) are capable of producing a lot of power, and offer

many advantages. The mechanical power generation equipment can be located at ground

level, which makes for easy maintenance. Also, VAWT are omni-directional, meaning

they do not need to be pointed in the direction of the wind to produce power. Finally,

there is potential for large power generation with VAWT because their size can be

increased greatly. However, there are also downfalls to the VAWT. Firstly, boundary

layer affects from the ground influence the air stream incident on the VAWT, which in

some cases leads to inconsistent wind patterns. Secondly, VAWT are not self-starting;

currently, an outside power source is required to start turbine rotation until a certain

rotational speed is reached.

The main objective of this project is to design and build a self-starting vertical axis wind

turbine. This report outlines the first term efforts in the design of our full-scale VAWT,

which is to be built early in the second term.

The self-starting issues surrounding VAWT will be tackled by the use of alternative blade

profiles and pitching mechanisms. A model that carries out turbine theory calculations

was created to aid in the design of the full-scale turbine. The model inputs include NACA

0012 airfoil lift and drag coefficients, angles of attack and relative wind speeds as

determined from a MATLAB program, and user inputs such as wind speed, tip speed

ratio, overall blade and turbine dimensions, and power required. The model outputs

forces and torques produced over a wide range of TSR. The model also uses various

angles of attack to determine performance results when pitching is used. Analysis results

indicated that passive pitching is an affecting way to boost the turbines ability to self-

start. However, the NACA 0012 profile was unable to achieve self-starting status, as it

iii

does not have large lift coefficients at low Reynolds numbers. It was concluded that a

profile with large lift at low speeds used along with passive pitching could achieve self-

starting status. As a result, three blade profiles will be tested and compared over the

holiday break in the wind tunnel facility at Dalhousie University. Results from prototype

testing in the wind tunnel will reveal the blade profile that offers the best performance for

self-starting.

The full-scale VAWT will be approximately 10ft tall, with a blade height of 5ft, and a

diameter of 8ft. Three blades will be CNC machined from aluminum stock. The full-scale

model will be built early next term to allow for adequate testing time.

To date the group has received $1000 from Richard Rachals, $600 from our Client, the

Mechanical Engineering Department, and $864 left over from the previous year wind

turbine design project. The primary expense of this project is the costs associated with

CNC machining the three aluminum blades. Other expenses include bearings, a

generation unit, and materials. To cut down on costs, equipment from previous year

design projects will be used where applicable.

iv

Table of Contents

Executive Summary ............................................................................................................ii List of Tables......................................................................................................................vi List of Figures ...................................................................................................................vii Glossary.............................................................................................................................. ix 1.0 Introduction ............................................................................................................. 1 1.1 Horizontal versus Vertical Axis Wind Turbines ................................................. 1 1.2 How Wind Energy is Harnessed ......................................................................... 3 1.3 How Turbines Work............................................................................................ 3 1.4 Turbine size as a function of power required. ..................................................... 5 1.5 Turbine Solidity as a Function of TSR ............................................................... 8 1.6 Chosen Sizing and Discussion ............................................................................ 9

2.0 Project Objective ................................................................................................... 11 3.0 Design Requirements ............................................................................................ 12 3.1 General Requirements ....................................................................................... 12 3.2 Costs and Usage ................................................................................................ 12 3.3 Timing and Intellectual Property....................................................................... 12

4.0 Design Process – Engineering Analysis Model .................................................... 13 4.1 Model Inputs ..................................................................................................... 13 4.2 Model Calculations ........................................................................................... 15 4.3 Model Outputs................................................................................................... 18 4.3.1 Number of Blades...................................................................................... 18 4.3.2 Active Pitching.......................................................................................... 23 4.3.3 Passive Pitching......................................................................................... 27

4.4 Analysis Conclusions ........................................................................................ 27 5.0 Design.................................................................................................................... 29 5.1 Base ................................................................................................................... 31 5.1.1 Steel Base .................................................................................................. 31 5.1.2 Plywood Base Extension........................................................................... 31 5.2.3 Steel Connecting Bracket .......................................................................... 31

5.2 Shaft .................................................................................................................. 32 5.3 Bearings............................................................................................................. 33 5.4 Center Mounts ................................................................................................... 34 5.5 Radial Connecting Arms ................................................................................... 35 5.6 Airfoils .............................................................................................................. 35 5.7 Blade Connecting Assembly ............................................................................. 35 5.8 Pitching Device ................................................................................................. 36 5.8.1 Linear Spring / Slotted Bracket Pitch System........................................... 36 5.8.2 Pitch Control Bracket to Manipulate the Pitch Angle............................... 38

7.0 Cost Analysis......................................................................................................... 43 8.0 Conclusions ........................................................................................................... 45 References ......................................................................................................................... 47 Appendix A - NACA 0012 Lift and Drag Coefficients .................................................... 49 Appendix B – Model Results (Numerical) For Pitch Angles at Various TSR.................. 56 Appendix C – MATLAB Programming Code for Analysis Model .................................. 64

v

Appendix D – Solid Edge Drawings ................................................................................. 66 Appendix E – Gantt Chart................................................................................................. 76

vi

LIST OF TABLES

Page No

Table 1.0 Typical Cp values for various wind turbines. 8

Table 1.1 Turbine sizing dimensions chosen for full-scale VAWT. 10

Table 4.0 Sizing spreadsheet for model inputs. 14

Table 4.1 Optimal pitch angles about the 360º turbine revolution for a

TSR of 0.75.

25

Table 7.0 Funding to date. 43

Table 7.1 Preliminary budget 44

vii

LIST OF FIGURES

Title Page No

Figure 1.0 GE Wind Energy’s 3.6 Megawatt HAWT. 2

Figure 1.1 An H-Darrius rotor VAWT 2

Figure 1.2 Force vectors for a HAWT. 4

Figure 1.3 Effects of angle of attack on lift 5

Figure 1.4 Rotor solidity as a function of TSR 9

Figure 4.0 Torque producing forces for 2 and 3-bladed turbines at a

TSR=0.25, and a pitch angle of 90º.

19



20



20



21

Figure 4.4 Torque producing forces for 2 and 3-bladed turbines at a TSR

of 0.25, and a pitch angle of 107º.

21



22



22



23

Figure 4.8 F1 fluctuation patterns for pitch angles of 95º, 105º and 107º at

a TSR of 0.75

24

Figure 4.9 Optimal pitch angles about the 360º turbine revolution for a

TSR of 0.75.

26

Figure 5.0 Full-scale VAWT assembly. 30

Figure 5.1 Existing turbine base structure from previous year design

projects.

32

Figure 5.2 Existing shaft from previous year design project. 33

Figure 5.3 Bearings from previous year design project. 34

Figure 5.4 Assembly drawing for blade attachments 36

viii

Title Page No

Figure 5.5 Linear spring pitch design 37

Figure 5.6 Slotted bracket for pitch design. 38

Figure 6.0 3-Blade H-type VAWT prototype for Dalhousie wind tunnel 40

Figure 6.1 Dalhousie University wind tunnel facility. 41

Figure 6.2 Existing prototype support arms. 41

Figure 6.3 NACA 0012 wooden profile before sanding and painting. 42

ix

GLOSSARY Angle of Attack Angle between chord of airfoil and apparent (relative) wind.

Blade Pitch Angle between blade chord and blade direction of travel.

Cut-In The rotational speed at which an alternator or generator starts

pushing electricity hard enough (has a high enough voltage) to

make electricity flow in a circuit.

Darrieus A Vertical Axis Wind Turbine design from the 1920s and

1930s by F.M. Darrieus, a French wind turbine designer.

Drag In a wind generator, the force exerted on an object by moving

air. Also refers to a type of wind generator or anemometer

design that uses cups instead of a blade or airfoil.

H-Rotor A Vertical Axis Wind Turbine design with straight blades

(usually vertical blades).

HAWT Horizontal Axis Wind Turbine

Horizontal Axis Wind

Turbine

A "normal" wind turbine design, in which the shaft is parallel

to the ground, and the blades are perpendicular to the ground.

Leading Edge The edge of a blade that faces toward the direction of rotation.

Leeward Away from the direction from which the wind blows.

Lift The force exerted by moving air on asymmetrically-shaped

wind generator blades at right angles to the direction of

relative movement. Ideally, wind generator blades should

produce high Lift and low Drag.

Load Something physical or electrical that absorbs energy. A wind

generator that is connected to a battery bank is loaded. A

disconnected wind generator is NOT loaded, so the blades are

free to spin at very high speed without absorbing any energy

from the wind, and it is in danger of destruction from over-

speeding.

Rotor The blade and hub assembly of a wind generator.

Shaft The rotating part in the center of a wind generator or motor

that transfers power.

Start-Up The wind speed at which a wind turbine rotor starts to rotate.

It does not -- necessarily produce any power until it reaches

cut-in speed.

Trailing Edge The edge of a blade that faces away from the direction of

rotation.

TSR Tip Speed Ratio – Ratio of blade speed to undisturbed wind

speed.

Undisturbed Wind That which occurs naturally.

VAWT Vertical Axis Wind Turbine

x

Variable Pitch A type of wind turbine rotor where the attack angle of the

blades can be adjusted either automatically or manually.

Vertical Axis Wind

Turbine

A wind generator design where the rotating shaft is

perpendicular to the ground and the cups or blades rotate

parallel to the ground.

Windward Toward the direction from which the wind blows.

Yaw Rotation parallel to the ground. A wind generator yaws to face

winds coming from different directions.

1

1.0 INTRODUCTION

With the recent surge in fossil fuels prices, demands for cleaner energy sources, and

government funding incentives, wind turbines are becoming a more viable technology for

electrical power generation. Fortunately there is an abundance of wind energy to be

harnessed. Currently, horizontal axis wind turbines (HAWT) dominate commercially

over vertical axis wind turbines (VAWT). However, VAWT do have some advantages

over HAWT.

1.1 Horizontal versus Vertical Axis Wind Turbines

The HAWT is the most common turbine configuration. The propellers and turbine

mechanisms are mounted high above the ground on a huge pedestal. It is a matter of taste

as to whether they enhance the landscape. However, there is no denying that the height at

which their mechanisms are located is a disadvantage when servicing is required. Also,

they require a mechanical yaw system to orient them such that their horizontal axis is

perpendicular to and facing the wind. As potential power generation is related to the

swept area (diameter) of the rotor, more power requires a larger diameter. The blades

experience large thrust and torque forces, so size is limited by blade strength. Figure 1.0

shows GE Wind Energy’s 3.6 Megawatt HAWT. Larger wind turbines are more efficient

and cost effective.

2

Figure 1.0. GE Wind Energy’s 3.6 Megawatt HAWT. [ref,1]

A VAWT does not need to be oriented into the wind and the power transition

mechanisms can be mounted at ground level for easy access. Figure 1.1 shows a picture

of an H-Darrius Rotor VAWT.

Figure 1.1. An H-Darrius rotor VAWT. [ref,2]

3

The perceived disadvantage of the VAWT is that they are not self-starting. However, it

could be argued that the HAWT is also not self-starting since it requires a yaw

mechanism for orientation. Currently, VAWT are usually rotated automatically until they

reach the ratio between blade speed and undisturbed wind speed (Tip Speed Ratio or

TSR) that produces a torque large enough to do useful work. Through the use of drag

devices and/or variable pitch blade designs, it is hoped that a VAWT will be able to reach

the required TSR without the use of a starter.

1.2 How Wind Energy is Harnessed

Turbines relying on drag, such as the anemometer and Savonius models, cannot spin

faster than the wind blows and are thus limited to a TSR of less than 1. Other turbines,

such as the Darrieus, rely on lift to produce a positive torque. Lift type wind turbines can

experience TSR as high as 6. This is possible because the natural wind is vector summed

with the wind opposing the forward velocity of the airfoil. This combined velocity is

known as the relative wind.

1.3 How Turbines Work

The wind imposes two driving forces on the blades of a turbine; lift and drag. A force is

produced when the wind on the leeward side of the airfoil must travel a greater distance

than that on the windward side. The wind traveling on the windward side must travel at a

greater speed than the wind traveling along the leeward side. This difference in velocity

creates a pressure differential. On the leeward side, a low-pressure area is created, pulling

the airfoil in that direction. This is known as the Bernoulli’s Principle. Lift and drag are

the components of this force vector perpendicular to and parallel to the apparent or

relative wind, respectively. By increasing the angle of attack, as shown in figure 1.2, the

distance that the leeward air travels is increased. This increases the velocity of the

leeward air and subsequently the lift. The Bernoulli Principle is illustrated in figure 1.3.

4

Figure 1.2. Force vectors for a HAWT. [ref,9]

5

Figure 1.3. Effects of angle of attack on lift. [ref,4]

Lift and drag forces can be broken down into components that are perpendicular (thrust)

and parallel (torque) to their path of travel at any instant. The torque is available to do

useful work, while the thrust is the force that must be supported by the turbine’s

structure.

1.4 Turbine size as a function of power required.

The power of the wind is proportional to air density, area of the segment of wind being

considered, and the natural wind speed. The relationships between the above variables are

provided in equation [1] below [ref, 10].

6

Pw = ½ ρAu3 [1]

where

Pw: power of the wind (W)

ρ: air density (kg/m3)

A: area of a segment of the wind being considered (m2)

u: undisturbed wind speed (m/s)

At standard temperature and pressure (STP = 273K and 101.3 KPa), equation [1] reduces

to:

Pw = 0.647Au3 [2]

A turbine cannot extract 100% of the winds energy because some of the winds energy is

used in pressure changes occurring across the turbine blades. This pressure change causes

a decrease in velocity and therefore usable energy. The mechanical power that can be

obtained from the wind with an ideal turbine is given as:

Pm = ½ ρ(16/27 Au3) [3]

where

Pm: mechanical power (W)

In equation [3], the area, A, is referred to as the swept area of a turbine. For a VAWT,

this area depends on both the turbine diameter and turbine blade length. For an H-type

VAWT the equation for swept area is:

As = Dt lb [4]

where

As: swept area (m2)

Dt: diameter of the turbine (m)

lb: length of the turbine Blades (m)

7

The constant 16/27 = 0.593 from equation [3] is referred to as the Betz coefficient. The

Betz coefficient tells us that 59.3% of the power in the wind can be extracted in the case

of an ideal turbine. However, an ideal turbine is a theoretical case. Turbine efficiencies in

the range of 35-40% are very good, and this is the case for most large-scale turbines. It

should also be noted that the pressure drop across the turbine blades is very small, around

0.02% of the ambient air pressure.

Equation [3] can be re-written as

Pm = Cp Pw [5]

where

Cp: coefficient of performance.

The coefficient of performance depends on wind speed, rotational speed of the turbine

and blade parameters such as pitch angle and angle of attack. The pitch angle for a

HAWT is the angle between the blades motion and the chord line of the blade, whereas

for a VAWT the pitch angle is between the line perpendicular to the blades motion and

the chord line of the blade. The angle of attack is the angle between the relative wind

velocity and the centerline of the blade. For fixed pitch turbines, these angles do not

change and the Cp is directly related to the TSR. See table 1 for typical Cp values for

various types of wind turbines.

8

Table 1.0. Typical Cp values for various wind turbines. [ref,3]

Example Calculation 1.0: If we take the average wind speed to be 6 m/s (5-7 m/s for Halifax), and consider a turbine 2.5m in diameter and 1.5m high, the power of the wind is,

Pw = 0.647(2.5m)(1.5m)(6m/s)3 = 524 (W)

However, we know from the Betz coefficient that Pw cannot be obtained. Using a Cp = 0.1 (10% efficiency) and the value of Pw (524 W) calculated above, we can see that for a 2.5m x 1.5m turbine in 6 m/s wind at STP, the mechanical power realized is:

Pm = 0.1(524W) = 52.4 W These equations can also be used to calculate the frontal area required from the output power required, wind speed, and the efficiency estimate. Then, the linear dimensions needed to support that frontal area are calculated. Generally, for both the eggbeater Darrieus and the straight–blade design, the height roughly equals the diameter.

1.5 Turbine Solidity as a Function of TSR

The operating tip–speed ratio (TSR) for a Darrieus rotor lies between 4 and 6. This

design TSR then determines the solidity, gear ratios, generator speeds, and structural

design of the rotor. Using this TSR and the graph in figure 1.4, a value of the solidity is

selected. As with the prop–type rotor, the solidity allows for the calculation of blade area.

Solidity times the rotor frontal area gives the total blade area. Dividing the total blade

area by the number of blades (usually 2 or 3) gives the individual blade area. The

individual blade area divided by the rotor height gives the chord length [ref,3].

Wind

System

Efficiency, %

simple

Construction Optimum

Design

Multibladed farm water pump

Sailwing water pump

Darrieus water pump

Small prop-type windcharger

(up to 2kW)

Medium prop-type windcharger

(2 to 10 kW)

Large prop-type wind generator

(over 10 kW)

Darrieus wind generator

10 30

10

15

10

20

----

15

25

30

20Savonius windcharger

20 30

30

30 to 45

35

9

Figure 1.4. Rotor solidity as a function of TSR. [ref,3]

1.6 Chosen Sizing and Discussion

The dimensions for the VAWT being built for this project are given in Table 1.1. The

diameter (2.56 m) is larger than the height (1.5m) to provide a longer chord length for the

same solidity. This design selection provides an increased Reynolds number for the flow

over the blades, and subsequently, increases the lift. Also, given the large thrust forces

involved, a shorter airfoil length will be less likely to undergo bend.

10

Table 1.1. Turbine sizing dimensions chosen for full-scale VAWT.

Inputs

Undisturbed Wind Speed 6 m/s

Density of air 1.204 kg/m3

Viscosity of air 1.81E-05 Ns/m2

TSR 4

Solidity 0.15

Number of Airfoils 3

Blade Height 1.50 m

Power required 50 watts

Estimated Coefficient of Performance

0.1

Outputs

Required swept area 3.85 m2

Diameter 2.56 m

Chord Length 0.13 m

Estimated weight/blade 7.67 Kg

RPM 179

Reynolds Number 204625

11

2.0 PROJECT OBJECTIVE

The objective of this project is to design and build a self-staring vertical axis wind turbine

that is capable of producing power in real world situations. The design of the turbine will

include exploration of various self-starting options, as well as construction of both model

and full-scale turbines. The full-scale turbine will be designed such that it can be

connected to a generator and a torque transducer to measure the output power, torque and

rotational speed of the turbine. The design will also allow for data collection regarding

the effects of blade pitch angles. With these applications, it is hoped that Dalhousie

University’s Department of Mechanical Engineering will conduct future research

involving vertical axis wind turbines.

12

3.0 DESIGN REQUIREMENTS

The design requirements for this project have been agreed upon with Dr. Murat Koksal

and the mechanical engineering department. These objectives were submitted earlier in

the term in a design requirements memo, and are summarized below.

3.1 General Requirements

� The VAWT will be an self-starting H-Type

� It will self-start using wind power only

� It will have blade dimensions of 1.5m (4.9’) high by 2.5m (8.1’) diameter

� It will be made of lightweight components like aluminum

� It will be designed to connect to an electrical generator to measure power output

� It will be rated to produce 50W at average Nova Scotia wind speeds (5-7 m/s)

3.2 Costs and Usage

� The budget for the project is $4000-$5000

� Turbine will be able to perform in outdoor, NS environment

� Life expectancy of 5 years with proper maintenance

� All mechanical components will be located at ground level

� The system will be easy to assemble

3.3 Timing and Intellectual Property

� Exploration of various options for self-starter designs, testing of self-starter

design ideas with mock up models in the wind tunnel, and design of the wind

turbine will be completed in the Fall term

� Building and testing of the full-scale prototype will be completed in the winter

term

� The finished product and intellectual property will belong to our client,

Mechanical Engineering Department, Dalhousie University

13

4.0 DESIGN PROCESS – ENGINEERING ANALYSIS MODEL

Self-starting is the major obstacle to be overcome for successful design of a VAWT. It

has been suggested [ref,5] that pitching the turbine blades such that the pitch angle is not

90 degrees allows for self-starting. To understand the physics surrounding pitching, an in

depth engineering analysis was carried out for a common airfoil profile, NACA 0012.

Performance data and characteristics for the symmetric NACA 0012 airfoil are available

for analysis as the airfoil is commonly used in various applications. The next series of

paragraphs explain the steps involved in the engineering analysis of the NACA 0012

airfoil with various pitching arrangements.

4.1 Model Inputs

A model was assembled so that various inputs were used to influence and generate

desired outputs that described the turbines performance. The Model is Excel based, with

a MATLAB program for calculating additional information. The design team created the

model to produce desired outputs from available inputs, and to avoid conducting

repetitions and lengthy calculations by hand.

Model inputs were primarily controlled by a sizing spreadsheet as shown in table 4.0. The

key inputs of the sizing spreadsheet include TSR, and solidity, as solidity has effects on

the chord length and blade height of the airfoil. The wind speed was kept constant

throughout the engineering analysis at the average wind speed value for Nova Scotia of

6m/s.

14

Table 4.0. Sizing spreadsheet for model inputs.

Inputs

Undisturbed Wind Speed 6 m/s

Density of air 1.204 kg/m3

Viscosity of air 1.81E-05 Ns/m2

TSR 4

Solidity 0.15

Number of Airfoils 3

Blade Height 1.50 m

Power required 50 watts

Estimated Coefficient of Performance

0.1

Another model input was the NACA 0012 airfoil lift and drag coefficients, [ref,6]. These

coefficients were supplied for various Reynolds numbers, and were input into the model

as a lookup table. NACA 0012 lift and drag coefficients are supplied in Appendix A.

The primary objective of the engineering analysis model was to understand the effects of

blade pitching. Therefore, pitch angles were another required input for the model. It is

known that during high rotational speeds, the most efficient operation of the turbine

occurs when the pitch angle is zero, or stated another way; the angle of attack is 90 º. As

a result, blade pitching is only necessary during start up when large torques are needed. A

range of pitch angles was chosen for the model analysis to determine how different

angles affected performance. The range was input into the model as angles of attack that

would be added to a pitch angle of 90º, and included angles of attack of -10, -5, -2, 0, 2,

5, 10, 12, 15, and 17. These 10 angles of attack resulted in pitch angles ranging from 80º

to 107º. The reason for not choosing larger or smaller pitch angles was that eventually the

blade would have to return to 90º. Angles further from the range chosen would involve a

large angle change and would likely induce turbulent flow over the airfoil.

15

4.2 Model Calculations

After the inputs are specified, the next step of the analysis involves calculations. The first

calculation was to determine the Reynolds number associated with the flow over the

airfoils. The equation for Reynolds number is given below as

air

air clTSRW

υρ ×××

=Re [6]

where

Re: Reynolds number

W: wind speed (m/s)

TSR: tip speed ratio

ρair: density of air (kg/m3)

cl: chord length (m)

ν air: viscosity of air (Ns/m2)

Because the turbine is spinning about a central shaft, the wind speed that the blades

experience is not equal to the ambient wind speed. The angle of attack of the turbine

blades is continuously changing throughout the blades’ 360º revolution. As a result, the

magnitude of the relative wind speed changes throughout rotation, and is the parameter

used to calculate the Reynolds number as given in equation [6]. Because the relative wind

speed changes for each degree of the 360º revolution, and also changes for different

values of TSR, it would be monotonous to carry out the calculations for relative wind

speed by hand. To avoid iterative calculations, a MATLAB program was written to

automatically calculate the angles of attack and the relative wind speeds for a specified

TSR throughout the revolution of 0º to 360º. The MATLAB program was only able to

output angles of attach and relative wind speeds for one TSR; therefore, the program had

to be run numerous times to obtain angles of attack and relative wind speeds for TSR

ranging from 0.25 through to 7. The MATLAB output file was converted to an Excel file

16

and added to the analysis model. The MATLAB code for the mentioned programs is

provided in Appendix C.

The model used the relative wind speed as specified by MATLAB to calculate the

Reynolds number as given by equation [6]. After the Reynolds number is calculated, the

lift and drag coefficients can be obtained from the NACA 0012 coefficients look up

tables. However, lift and drag coefficients are dependant on the Reynolds number and the

angle of attack. To calculate the angle of attack, the angle specified from the MATLAB

program is added to the desired blade pitching angle of attack, as specified in the model

inputs. Because there are ten angles of attack being considered for the pitching analysis, it

is necessary to carry out all calculations for ten scenarios. Once the actual angle of attack

is determined, the model uses the Reynolds number along with the angle to lookup the

appropriate lift and drag coefficients. When the lift and drag coefficients are determined,

the lift and drag forces can be calculated using the following equations, respectively.

daird

lairl

CblclWF

CblclWF

×××=

×××=

2

2

2

1

2

1

ρ

ρ [7, 8]

where

Fl: lift force (N)

Fd: drag force (N)

bl: blade length (m)

Cl: lift coefficient

Cd: drag coefficient

The lift and drag forces were then resolved into components parallel and perpendicular to

the blades’ path of rotation. The following four equations were used to resolve the lift and

drag forces into parallel and perpendicular components.

17

=

=

−

=

−

=

180sin

180cos

180180

90sin

180180

90cos

,

,

,

,

πα

πα

παπ

παπ

actualdcircd

actualdhurtd

actual

lcircl

actuallhlepl

FF

FF

FF

FF

[9, 10, 11, 12]

where

:,helplF Force in direction of travel (N)

:,circlF Force contributing to centrifugal force (N)

:,hurtdF Force opposing motion of blade travel (N)

:,circdF Force contributing to centrifugal force (N)

:actualα Angle of attack with added pitching (rad)

Finally, parallel forces are added, and perpendicular forces are added to obtain

expressions for F1 and F2, as given by equations [8] and [9].

circdcircl

hurtdhelpl

FFF

FFF

,,2

,,1

+=

−= [13, 14]

where

F1: forces contributing to torque (N)

F2: centrifugal forces (N)

The resulting forces, F1 and F2, are the forces experienced by a turbine with one blade

rotating about a central axis. To obtain the forces experienced by a turbine with 2 blades,

the forces are split at 180º and doubled. For example, the forces experienced by the first

18

blade at 90º are the same forces to be experienced by the 2nd blade at 270º. This was also

done for a 3-blade turbine; however, the forces were split at 120º, and added three times.

As mentioned previously, there are ten angles of attack considered for this analysis. As a

result, the above analysis was carried out for each angle to be considered, and also for

TSR ranging from 0.25 to 7. This range of TSR coverage provided a complete picture of

how pitching effects turbine performance from start up to high rotational speeds.

4.3 Model Outputs

The major results from the engineering analysis Model are stated below. Graphs are used

to illustrate key points.

4.3.1 Number of Blades

Before choosing a final VAWT design, it was necessary to determine the number of

blades the turbine would have. For a 2-blade turbine, there are times when both blades

are in a position such that the wind does not encourage rotation. This is known as the stall

position. For a 3-blade turbine, the stall condition is eliminated. This is a conceptual

reasoning; however, the analysis model was used to test this conceptual reasoning.

The original analysis in the model determined the overall forces for a one-bladed turbine.

These forces were easily manipulated to represent overall forces for a 2 and 3-blade

turbine. The results showed that the 2-blade turbine generally produces a smaller average

F1 than the 3-bladed design. For a 90º pitch angle, there are TSR ranges where the 2-

blade design produces larger F1 than the 3-blade; however, because the blades can be

pitched at this low TSR range, and pitched blades produce a more favorable F1 result, it

is noted that the 3-blade design is still superior to the 2-blade design. As a result, the 3-

blade design was chosen for the full scale VAWT design. Figures 4.0 through 4.3

illustrate the torque producing forces, F1, experienced by 2 and 3-bladed turbines for TSR

of 0.25, 1, 2 and 3. The pitch angle for figures 4.0 through 4.3 is kept constant at 90º so

that the only variable among the figures is the TSR. Figures 4.4 though 4.7 illustrate the

19

F1 forces experience by 2 and 3-blade designs at TSR of 0.25, 1, 2, and 3 as well;

however, figures 4.4 through 4.7 are taken at pitch angles other than 90º. It is noted that

at TSR below 3, the optimal pitch angle (the pitch angle producing the largest F1), is

107º, while at TSR higher than 3 have optimal pitch angles closer to 90º.

Torque Producing Forces for 2 and 3 blade Turbines

TSR=0.25, Pitch Angle = 90 degrees

-0.40

-0.20

0.00

0.20

0.40

0.60

0.80

1.00

0 30 60 90 120 150 180 210 240 270 300 330 360

Position of Revolution (degrees)

Torque Producing Force, F1 (N)

2-blade 3-blade Linear (3-blade) Linear (2-blade)

Figure 4.0. Torque producing forces for 2 and 3-bladed turbines at a TSR=0.25, and a pitch angle of 90º.

20



-1.00

-0.80

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

0.80

0 30 60 90 120 150 180 210 240 270 300 330 360







-4.00

-3.00

-2.00

-1.00

0.00

1.00

2.00

3.00

0 30 60 90 120 150 180 210 240 270 300 330 360





21



-5.00

-4.00

-3.00

-2.00

-1.00

0.00

1.00

2.00

3.00

4.00

5.00

0 30 60 90 120 150 180 210 240 270 300 330 360


Torque Producing Force,

F1 (N)





-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

0.80

1.00

1.20

0 30 60 90 120 150 180 210 240 270 300 330 360




Figure 4.4. Torque producing forces for 2 and 3-bladed turbines at a TSR of 0.25, and a pitch angle of 107º.

22



-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

2.00

0 30 60 90 120 150 180 210 240 270 300 330 360







-3.00

-2.50

-2.00

-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

2.00

2.50

0 30 60 90 120 150 180 210 240 270 300 330 360





23



0.00

2.00

4.00

6.00

8.00

10.00

12.00

0 30 60 90 120 150 180 210 240 270 300 330 360





4.3.2 Active Pitching

Active pitching involves the use of a mechanism or actuator to pitch the blades at various

instances about the blades 360˚ revolution such that the maximum F1 is obtained

throughout the entire revolution. As mentioned previously, the angle of attack

continuously changes throughout the 360º revolution of the blades around the turbine

shaft. As a result, the optimal pitch angle continuously changes. In some instances, the

optimal angle of attack changes in as little as 10º of blade revolution. Note that the

optimal angle of attack is defined as the angle of attack that gives the largest F1.

Physically changing the pitch angles every 5º or 10º of revolution is not physically

possible, especially at high rotational speeds. Also, the optimal angles of attack

sometimes vary between as low as 85º to as high as 105º in 5º of revolution. This is

highly impractical, not only in the physical sense, but also because it would disturb the

24

flow over the airfoil, causing turbulent flow and therefore not generating a continuous or

steady lift force.

Figure 4.8 shows F1 fluctuations about the 360º revolution for 5 different pitch angles at a

TSR of 0.75. It is clear from figure 4.8 that when certain pitch angles are at a low F1

value, other pitch angles achieve high F1. Table 4.1 shows the pitch angles that produce

the maximum F1 for every 5º of revolution. It can be seen from table 4.1 that the pitch

angle varies very frequently, which would relate to a constantly moving blade.

F1 Fluctuations for pitch angles of 95, 105 and 107 Degrees

TSR=0.75

-1.00

-0.50

0.00

0.50

1.00

1.50

2.00

2.50

0 30 60 90 120 150 180 210 240 270 300 330 360



95 deg 105 deg 107 deg

Figure 4.8. F1 fluctuation patterns for pitch angles of 95º, 105º and 107º at a TSR of 0.75.

25

Table 4.1. Optimal pitch angles about the 360º turbine revolution for a TSR of 0.75.

Turbine Position

(degrees)

Pitch Angle

(degrees) F1 (N)

Turbine Position

(degrees)

Pitch Angle

(degrees) F1 (N)

0 95 1.31 180 105 2.27

5 92 1.09 185 107 2.17

10 90 0.90 190 105 1.09

15 88 1.12 195 105 1.05

20 85 1.37 200 107 0.85

25 105 1.14 205 107 0.88

30 107 0.81 210 105 0.94

35 107 0.88 215 105 1.14

40 105 1.04 220 85 1.37

45 105 1.05 225 88 1.12

50 107 1.04 230 90 0.90

55 107 2.17 235 92 1.09

60 105 2.27 240 95 1.31

65 107 2.17 245 92 1.09

70 105 1.09 250 90 0.90

75 105 1.05 255 88 1.12

80 107 0.85 260 85 1.37

85 107 0.88 265 105 1.14

90 105 0.94 270 107 0.81

95 105 1.14 275 107 0.88

100 85 1.37 280 105 1.04

105 88 1.12 285 105 1.05

110 90 0.90 290 107 1.04

115 92 1.09 295 107 2.17

120 95 1.31 300 105 2.27

125 92 1.09 305 107 2.17

130 90 0.90 310 105 1.09

135 88 1.12 315 105 1.05

140 85 1.37 320 107 0.85

145 105 1.14 325 107 0.88

150 107 0.81 330 105 0.94

155 107 0.88 335 105 1.14

160 105 1.04 340 85 1.37

165 105 1.05 345 88 1.12

170 107 1.04 350 90 0.90

175 107 2.17 355 92 1.09

360 95 1.31

It is possible; however, to choose two pitch angles such that one angle is optimal while

the other is not, and vice-versa. If this can be done, and if the two pitch angles are within

a close range to each other, it could be practical to vary the pitch angle between these two

angles during the blades’ revolution. Figure 4.9 shows the average F1 for all ten pitch

26

angle inputs, at a TSR of 0.75. Pitch angles of 107º and 105º achieve the largest average

F1 values throughout their 360º revolution, as shown in figure 4.9. As a result, it would be

practical to vary the pitch angle from 105º to 107º degrees to maximize turbine

performance.

Average F1 for 10 Pitch Angles

TSR=0.75

-0.40

-0.20

0.00

0.20

0.40

0.60

0.80

1.00

0 30 60 90 120 150 180 210 240 270 300 330 360



80deg 85 deg 88 deg 90 deg 92 deg

95 deg 100 deg 102 deg 105 deg 107 deg

Figure 4.9. Average F1 for pitch angles of 80º through 107º for a TSR of 0.75.

To achieve this varying pitch, a mechanical device such as an actuator would be required.

As our design requirements specify that a self-starting turbine with no external power

sources will be fabricated, the outside power source needed to run the actuators would

violate the design requirements. As a result of the active pitching analysis, it is concluded

that continuously varying the pitching angle is, in many cases, not a practical solution to

achieve self-starting.

27

4.3.3 Passive Pitching

The idea of passive pitching is that an initial pitch angle other than 90º is set with a

spring, and when the turbine reaches a certain rotational speed, the forces from the blade

pull on the spring, extending it such that the blades achieve a pitch angle of 90º, again, to

achieve maximum performance. Results from the analysis model were used to determine

what pitch angle would be optimal before the turbine reached a desired speed where the

blades could return to 90º. From the analysis, it was determined that a pitch angle of 107

degrees provides the largest average torques over the range of TSR from 0.25 to 2.25. A

printout of the model results for various pitch angles from a TSR range of 0.25, to 7 are

provided numerically in Appendix B. These tables present the overall performance of

difference pitch angles at difference TSR, and they clearly show that the pitch angle of

107º is optimal for TSR below 2.25. The NACA 0012, however, experiences very low

torques around a TSR of 2, which represents the ‘deadband’ phenomenon. Although the

torques produced in this TSR range are positive, they are only slightly positive. After a

TSR of 2.25, the maximum average torque is obtained with pitch angles close to 88-90

degrees. Again, these results are shown in the tables in Appendix B.

4.4 Analysis Conclusions

As a result of the engineering analysis carried out for the NACA 0012 airfoil at various

pitch angles, it was shown that the ‘deadband’ phenomenon could be overcome, but only

slightly. To overcome the ‘deadband’ with a level on confidence, torques in the TSR

range of 0.75 to 2.75 must be increased to values further above zero. To achieve this, an

airfoil with high lift coefficients at low Reynolds numbers is needed. It has been

suggested that both the NACA 4415 [ref,7] and the NACA 0018 [ref,8] experience these

characteristics. The NACA 0018, another symmetric airfoil, has a fatter profile than the

NACA 0012, while the NACA 4415 is a cambered airfoil, meaning that the airfoil has a

curved shape rather than a symmetric one. Cambered blades are also thought to

experience better performance on small-scale turbines because the backwash from the

blades is aimed in the direction of successive blade travel. The team was unable to find

28

evidence to prove that the NACA 0018 and 4415 experience larger lift coefficients than

the NACA 0012 at low Reynolds numbers. However, data was found for the NACA 0018

and 4415 for high Reynolds numbers, and the trends in lift coefficients showed larger

values than the NACA 0012 experiences at the same high Reynolds number. Although it

is thought that these lift coefficient trends may continue into lower Reynolds numbers, it

is not known for certain. As the mentioned airfoils are usually used in applications with

fast wind speeds, the area of VAWT self-starting is fairly new so there is not a lot of

information available for low speed applications such as this. To determine which profile

has the best performance at low speeds, prototype testing will be carried out with the

three profiles as a means to compare performance data. Results from the prototype testing

will be used to determine which profile will be used for the full-scale model VAWT.

29

5.0 DESIGN

The components of the full-scale VAWT are listed below, in order of installation. See

figure 5.0 for the location of each component on the turbine assembly.

5.1 Base

5.2 Shaft

5.3 Bearings

5.4 Center Mounts

5.5 Radial Connecting Arms

5.6 Airfoils

5.7 Blade Connecting Assembly

5.8 Pitching Device

30

Base Shaft

Airfoils

Center

Mount

Blade Connecting

Assembly and Pitching

Device

Bearings

Radial Connecting

Arms

Figure 5.0. Full-scale VAWT assembly.

31

5.1 Base

The base from previous year design projects will be reused for our project. The existing

steel base will be modified with a steel connecting bracket and plywood base extension.

The base components are discussed below.

5.1.1 Steel Base

We plan to use the base from previous years design projects, with a few modifications.

The base is steel and stands approximately 3 feet high and weighs roughly 70 lbs, as

shown in figure 5.1. On its own the base will not support the torque and moments

produced from our wind turbine, so a base extension and a connecting bracket will be

required. A CAD drawing of the steel base is shown in Appendix D.

5.1.2 Plywood Base Extension

To modify the base, we are going to purchase 4 sheets of 4’ x 8’ x ¾” plywood to

construct a base extension that will give us a larger footprint on which to place weights.

A CAD drawing is provided in Appendix D. For our purposes, we have determined that

sandbags will be the optimal blend between weight, cost effectiveness, and

transportability. The plywood sheets will be oriented with 2 sheets side-by-side, with 2

other sheets on top at 90 degrees rotation to the bottom 2 sheets. This creates a

reinforced 8’ x 8’ base.

5.2.3 Steel Connecting Bracket

To connect the 4 sheets of plywood to the steel base we will use a bottom bracket made

of 1/8” x 2 ½ ” steel, as shown in Appendix D. This bottom bracket will be bolted from

the bottom up through the sheets of plywood and up through the steel base. This 36” x

36” structure will provide quick assembly and disassembly of the turbine base structure.

The bottom bracket will require 4 simple corner welds and flat head bolts welded in

position that will encourage quick assembly.

32

Figure 5.1. Existing turbine base structure from previous year design projects.

5.2 Shaft

The shaft from existing design projects will be used for our project. To minimize weight,

the 69 ½”, 1 ½”diameter section of the shaft will be milled down to 1 3/8” to make the

shaft uniform and to reduce weight. The existing shaft can be seen in figure 5.2, and a

CAD drawing of the shaft, showing the section to be milled, is provide in Appendix D.

33

Figure 5.2. Existing shaft from previous year design project.

5.3 Bearings

Minimizing required start-up torque is essential for the wind turbine to self-start and thus,

the success of our project. Without proper bearings our wind turbine will either not

operate properly, or ruin the bearings that were used improperly, which could result in

unsafe operating conditions. The bearings that were used in previous years wind turbine

design projects, shown in figure 5.3, are inferior units that are not salvageable. Bearings

can be very expensive, and for our particular setup we will require 2 roller bearings that

are going to primarily centralize the shaft, and a turntable bearing to take the majority of

the weight. This combination will provide the least amount of friction, while maximizing

bearing life and maintaining safe operating conditions.

34

Figure 5.3. Bearings from previous year design project.

5.4 Center Mounts

In order to connect the radial arms and the turbine blades to the center shaft, there needs

to be a strong connection that will withstand the centrifugal and inertial forces caused by

the rotation of the wind turbine. The center shaft mount, machined from aluminum, will

slide over the end of the shaft and will be fastened with setscrews, enabling quick

assembly and disassembly. The three radial arms will be bolted into the center mount via

female clamps at 120 degree angles of separation. This will be a one-piece unit, designed

using finite element analysis, to minimize weight and to reduce the possibility of failure.

A CAD drawing of the center mounts is provided in Appendix D.

35

5.5 Radial Connecting Arms

Aluminum will be used for the six radial connecting arms to maintain a lightweight

assembly with minimal inertial, moment, and centrifugal forces. The connecting arms

provide a means to mount the blades to the center mounts and thus the center shaft.

There will be two 3/8” bolts connecting each arm to the center mounts, while a pivoting

device allows the blade to pitch on the opposite end. The arms will be purchased as ½” x

1 ½ ” and may need to be cut to the appropriate 4’ lengths. The arm edges will be

rounded to reduce drag. A CAD drawing of the radial arms is provided in Appendix D.

5.6 Airfoils

Selecting appropriate airfoils for our 3-bladed vertical axis wind turbine is one of the

most important design decisions. Different profiles provide various advantages and

disadvantages that must be considered. Wind tunnel prototype testing results will provide

information that will be used to choose the optimal blade profile for a self-starting

application. Once a profile is selected, 3 blades will be CNC machined from aluminum

flat-bar into an accurate representation of the selected airfoil. The estimated weight of

each aluminum airfoil is 22 lbs. The top and bottom of each blade will be a 1” x 5” x 1”

deep rectangular section to allow for easier connections to the radial arms and passive

pitching system. A CAD drawing of the airfoils is provided in Appendix D.

5.7 Blade Connecting Assembly

The blade connecting assembly will be used to connect the blades to the radial arms. The

current design is to drill a 3/8” hole through the radial arm, and also into the blade to a

depth of 3”. A steel dowel will be used for the connection. A washer and bushing will be

located between the connecting arm and the top of the blade, and a set screw cap will

36

secure the blade to the radial connecting arm. A drawing of the blade connection

assembly is provided in figure 5.4.

Figure 5.4. Assembly drawing for blade attachments.

5.8 Pitching Device

Pitching the turbine blades is thought to improve turbine performance characteristics. The

following pitch design has been discussed; however, our chosen blade pitching design

will be determined in early January.

5.8.1 Linear Spring / Slotted Bracket Pitch System

For this design, a linear spring will be connected to the radial arm. It will initially be in

compression when the turbine is at rest, pulling the pointed end of the airfoil towards the

center of the turbine. As the turbine begins to rotate, the centrifugal forces will apply

tension to the spring, and the blade will gradually be let out. This design will be used in

37

conjunction with a slotted bracket to ensure that the blade pitches between the desired

pitch angles. Figure 5.5 shows the linear spring pitching design, while figure 5.6 shows

the slotted bracket. The first diagram in figure 5.5 shows the start-up blade orientation,

set at the optimal pitch angle of 107˚. As the TSR increases, the centrifugal forces

increase. When the TSR reaches 3, the centrifugal force will be enough such that the

force causes the spring to extend until the pitch angle is 90˚. Also incorporated into the

linear spring pitch design will be a stop mechanism such that the blade is not able to

rotate to a pitch angle smaller than 90˚. This stop will be designed such that the forces on

the blade while it is in the 90˚ position will not be held by the spring. The stopping device

will also be used to withstand the centrifugal forces for this condition.

Figure 5.5. Linear spring pitch design.

38

Slotted

Bracket

Figure 5.6. Slotted bracket for pitch design.

5.8.2 Pitch Control Bracket to Manipulate the Pitch Angle

For this design, three pitching control brackets will be machined from aluminum as seen

in figure 14. These brackets will be bolted to the top radial arms and will have a series of

holes drilled to correspond to different pitching angles. The blade will have a pin in the

top to align with the bracket holes. The slotted bracket is shown in figure 5.6.

39

6.0 STATUS

Testing will be the major factor that determines the blade profile for the full-scale

turbine. Currently, there are plans to test three different blade profiles that were selected

based on high Reynolds number performance characteristics. The three blade profiles are

� NACA 0012

� NACA 0018

� NACA 4415

The existing three blade H-type VAWT set-up from last years Wind Turbine Tester

design project will be used for testing, as it has already been designed for use with the

University’s wind tunnel and torque transducer. The existing 3-blade H-type VAWT

prototype can be seen in figure 6.0, and the wind tunnel is shown in figure 6.1. Due to the

three blade profiles, modifications to existing support arms shown in figure 6.2 will be

required. Alterations will involve removal of the rounded end portion of the supports, and

the existing holes may have to be drilled again. The group plans to contact Stewart Carr

to perform this work. The test blades will be made from clear pine, using a table saw to

cut out a rough profile for each blade shape. Albert Murphy has volunteered to do this

work. The profiles will then be sanded by hand and painted with oil based paint to obtain

a smooth profile. Figure 6.3 shows the NACA 0012 wooden blade profile before sanding

and painting. Each set of blades will be manufactured from one piece of pine, then cut to

their appropriate 1’ lengths, in an effort to make each set of blades as uniform as possible.

The blades will be bolted to the supports and a series of nuts will be used to position them

radially and vary the pitch angle.

40

Figure 6.0. 3-Blade H-type VAWT prototype for Dalhousie wind tunnel.

41

Figure 6.1. Dalhousie University wind tunnel facility.

Figure 6.2. Existing prototype support arms.

42

Figure 6.3. Pictures of the prototype NACA 0012 wooden profile before sanding and painting.

Prototype testing will begin when Christmas exams are completed. The current plan is to

test each set of blades at low wind speeds (up to ~6 m/s) and measure torque, rotational

speed, acceleration time, and maximum tip speed ratio for each set of blades. Also,

results using different pitch angles will be obtained for each set of blades.

Once the results of the tests are known, the blade profile with the best results will be

chosen for use in the full-scale version of the turbine.

43

7.0 COST ANALYSIS

A preliminary budget of $4000-$5000 has been set. The main costs include the aluminum

stock ($1000), bearings ($300), plywood ($310) and CNC machining time ($2000). Other

minor items, such as setscrews, bolts, nuts, and washer hope to be obtained at a low cost.

In addition, the aluminum stock and plywood hope to be obtained at lower costs through

the department. A detailed budget can be seen in table 7.1.

Currently, the team has $2464 of funds available, and these come from three sources.

First, $864 has been donated from a previous wind turbine project. Second, the

mechanical engineering department has donated $600. Finally, $1000 has been donated

by Richard Rachals, a retired engineer who lives in Lunenburg, N.S. However, the money

from the previous design project and the department has to spend on the CNC machining

of the aluminum airfoils. A summary of donations can be seen in table 7.0.

Other sources of funding have also been undertaken. Currently, wind energy companies

and organizations, private businesses, and government have been contacted with regard

to funding the project.

Table 7.0. Funding to date.

Who Amount

Previous Design Project $8641

Mechanical Dept. $6001

Richard Rachals $1000 1Must be spent on CNC machining

44

Table7.1. Preliminary budget

Materials (Known Parts)

Item Quantity Use Cost (CND)

1” x 6” x 6’ T-6061 Aluminum

3 Aluminum stock to manufacture the airfoils

$6102

½ ” x 1 ½ ” x 4’ T-6061 Aluminum

6 Aluminum stock to manufacture the radial arms

$1502

3” x 6” x 1’ T-6061 Aluminum

1 Aluminum stock to manufacture the center mount

$1502

1/8” x 6” x 2’ T-6061 Aluminum

1 Aluminum stock to manufacture the connecting brackets

$302

4’ x 8’ x ¾’ Thick Plywood 4 Used for the base $310

¼” x 2 ½” x 6’ Hot Rolled A-36 Steel

2 Used for base steel connecting bracket

$402

3/8” X 2’ HR CQ Steel Round 1 Dowel for blade assembly connection

$52

Linear Springs 3 Used in the pitching device $15

Bearings 3 Used for shaft support and alignment

$300 – Subject to Change

Sand TBD To weigh down the base $ 5/bag

Materials (To Be Determined)

Set Screws – Various Sizes 6 Connecting center mount to the shaft

TBD

Rod 3 Used in the passive pitch device

TBD

Nuts, Blots, Washers Connections TBD

Machining

Aluminum Machining Time To machine parts 3

Welding Time To weld parts 3

CNC Machining (At Dal) Time To machine the blades $20004 2 Source www.metalsdepot.com 3 Manual machining time provided by the technicians at no cost 4 Partially paid for by the department and previous years design project contributions

45

8.0 CONCLUSIONS

The first part of the design process, which included research, brainstorming, engineering

analysis, and turbine design selection was completed during the fall term. The initial

research and analysis portion of the project provided its share of complications; however,

once completed it provided valuable information about the final design. To date, the

major components of the turbine have been settled on, in particular, full-scale aluminum

blades have been chosen, and will be machined in the CNC lab at Dalhousie. There are

still some final design options that must be finalized, and these decisions will be made

before turbine construction begins in early January.

Testing will be a major part of the design selection, as blade profile selection will occur

over the Christmas break based on prototype testing results. The test results should

provide insight as to which blade profile provides the most torque and shows the most

significant effects due to blade pitching. In addition to prototype testing, finite element

analysis will be performed on each blade profile in an effort to confirm the wind tunnel

results. The blade connectors and pitching system designs will also be finalized, and a

spring selection for the passive pitching system will be made. A device used to couple the

torque transducer and generator to the shaft will be designed as well. This will occur in

conjunction with the selection of a generator, and design of a device that would couple

the generator to the turbine after it reaches a certain rotational speed. The last item to be

decided on is a brake mechanism that must be incorporated into the design for safety

reasons. These items will be decided on before issuing of the second build report in

January.

Construction of the full-scale turbine will begin during the first week of the winter term,

with the goal of finishing the final product by the end of February. This will allow for a

month of testing and data analysis, as well as provide time for making any design

alterations that are needed. A project timeline for the second term can be seen in the

Gantt chart in Appendix E. Based on current progress, the group is confident that the

final product will meet all the requirements set out in the fall term.

46

Finally, the group will like to thank Dr. Murat Koksal and Dr. Larry Hughes for their

ongoing guidance, as well as the Mechanical Engineering Department technicians for

their help with prototype testing. Thanks are also extended to Richard Rachals and the

Mechanical Engineering Department for their donations to the project.

47

REFERENCES

1. U.S. Department of Energy. “Wind and Hydropower Technologies Program”.

Retrieved from http://eereweb.ee.doe.gov/windandhydro/wind_how.html in

November, 2005.

2. Wikipedia Encyclopedia. Retrieved from http://en.wikipedia.org/wiki/Image:H-

Darrieus-Rotor.png.jpg on November 28, 2005.

3. Chang, Professor L..(2005) “Advanced Topics in Environmental Engineering -

Wind Power,” Ch 4. University of New Brunswick. Retrieved from

http://www.ece.unb.ca/powereng/courses/EE6693/index.html in October, 2005.

4. EarthLink (2005). “See How it Flies – A new spin on the perceptions, procedures,

and principles of flight.” Retrieved from

http://www.av8n.com/how/htm/airfoils.html in November 2005.

5. Kirke, Brian Kinloch, 1998. “Evaluation of Self-Starting Vertical Axis Wind

Turbines for Stand-Alone Applications”. Griffith University, Australia. Retrieved

from http://www4.gu.edu.au:8080/adt-root/public/adt-QGU20050916.120408/ on

November 1, 2005.

6. Sheldahl, Robert E., Klimas, Paul C., 1981. “Aerodynamic Characteristics of

Seven Symmetrical Airfoil Sections Through 180-Degree Angle of Attack for Use

in Aerodynamic Analysis of Vertical Axis Wind Turbines”, Sandia National

Laboratories, Albuquerque, NM., USA.

7. Reuss, R.L., Hoffmann, M.J., Gregorek, G.M., December 1995. ‘Effects of

Surface Roughness and Vortex Generators on the NACA 4415 Airfoil, The Ohio

48

State University, Columbus, Ohio, USA. Retrieved from

http://wind.nrel.gov/OSU_data/reports/7x10/N4415_7x10.pdf on November 3,

2005.

8. Pawsey, N.C.K., 2002. “Development and Evaluation of Passive Variable-Pitch

Vertical Axis Wind Turbines”, School of Mechanical and Manufacturing

Engineering, The University of South Wales, Australia.

9. Gipe, Paul, 2004. “Wind Power,” Chelsea Green Publishing Company, Page 97

10. Johnson, Dr. Gary L. (November 21, 2001) “Wind Turbine Power – Ch 4. Wind

Turbine Power, Energy and Torque.” Retrieved from

http://www.eece.ksu.edu/~gjohnson/wind4.pdf in October 2005.

49

APPENDIX A - NACA 0012 LIFT AND DRAG COEFFICIENTS

The following tables list the lift and drag coefficients for the NACA 0012 airfoil at Reynolds numbers varying from 10,000 to 5,000,000. [ref,6]

Re 10000 Re 20000

# alpha Cl Cd # alpha Cl Cd

1 0 0 0.0337 1 0 0 0.0245

2 1 0.083 0.0338 2 1 0.1057 0.0247

3 2 0.1534 0.0343 3 2 0.2072 0.0251

4 3 0.2009 0.0351 4 3 0.3032 0.0259

5 4 0.2003 0.0359 5 4 0.3929 0.027

6 5 0.0328 0.0351 6 5 0.4781 0.0282

7 6 -0.1413 0.046 7 6 -0.0298 0.046

8 7 -0.1142 0.058 8 7 -0.1089 0.058

9 8 -0.0703 0.072 9 8 -0.0699 0.072

10 9 -0.0215 0.086 10 9 -0.0198 0.086

11 10 0.0311 0.101 11 10 0.032 0.101

12 11 0.0848 0.117 12 11 0.0856 0.117

13 12 0.1387 0.134 13 12 0.1894 0.134

14 13 0.1928 0.152 14 13 0.1934 0.152

15 14 0.2468 0.171 15 14 0.2474 0.171

16 15 0.3008 0.19 16 15 0.3014 0.191

17 16 0.3548 0.21 17 16 0.3554 0.21

18 17 0.4079 0.231 18 17 0.4089 0.23

19 18 0.4606 0.252 19 18 0.462 0.252

20 19 0.5121 0.274 20 19 0.5147 0.274

21 20 0.5838 0.297 21 20 0.5663 0.297

22 21 0.6161 0.32 22 21 0.6184 0.32

23 22 0.6687 0.344 23 22 0.6709 0.344

24 23 0.7216 0.369 24 23 0.7238 0.369

25 24 0.7744 0.394 25 24 0.7765 0.394

26 25 0.8276 0.42 26 25 0.8297 0.42

27 26 0.881 0.446 27 26 0.8831 0.446

28 27 0.9345 0.473 28 27 0.9365 0.473

29 30 0.915 0.57 29 30 0.915 0.57

30 35 1.02 0.745 30 35 1.02 0.745

31 40 1.075 0.92 31 40 1.075 0.92

32 45 1.085 1.075 32 45 1.085 1.075

33 50 1.04 1.215 33 50 1.04 1.215

34 55 0.965 1.345 34 55 0.965 1.345

35 60 0.875 1.47 35 60 0.875 1.47

36 65 0.765 1.575 36 65 0.765 1.575

37 70 0.65 1.665 37 70 0.65 1.665

38 75 0.515 1.735 38 75 0.515 1.735

39 80 0.37 1.78 39 80 0.37 1.78

40 85 0.22 1.8 40 85 0.22 1.8

41 90 0.07 1.8 41 90 0.07 1.8

42 95 -0.07 1.78 42 95 -0.07 1.78

50

43 100 -0.22 1.75 43 100 -0.22 1.75

44 105 -0.37 1.7 44 105 -0.37 1.7

45 110 -0.51 1.635 45 110 -0.51 1.635

46 115 -0.625 1.555 46 115 -0.625 1.555

47 120 -0.735 1.465 47 120 -0.735 1.465

48 125 -0.84 1.35 48 125 -0.84 1.35

49 130 -0.91 1.225 49 130 -0.91 1.225

50 135 -0.945 1.085 50 135 -0.945 1.085

51 140 -0.945 0.925 51 140 -0.945 0.925

52 145 -0.91 0.755 52 145 -0.91 0.755

53 150 -0.85 0.575 53 150 -0.85 0.575

54 155 -0.74 0.42 54 155 -0.74 0.42

55 160 -0.66 0.32 55 160 -0.66 0.32

56 165 -0.675 0.23 56 165 -0.675 0.23

57 170 -0.85 0.14 57 170 -0.85 0.14

58 175 -0.69 0.055 58 175 -0.69 0.055

59 180 0 0.025 59 180 0 0.025

Re 40000 Re 80000


1 0 0 0.0175 1 0 0 0.0133

2 1 0.11 0.0177 2 1 0.11 0.0134

3 2 0.22 0.0181 3 2 0.22 0.0138

4 3 0.3376 0.0189 4 3 0.33 0.0145

5 4 0.4464 0.0199 5 4 0.44 0.0155

6 5 0.5276 0.0218 6 5 0.55 0.017

7 6 0.6115 0.0232 7 6 0.6384 0.0189

8 7 -0.0212 0.058 8 7 0.7227 0.0204

9 8 -0.0615 0.072 9 8 0.693 0.0222

10 9 -0.016 0.086 10 9 -0.001 0.06

11 10 0.0344 0.101 11 10 0.0413 0.06

12 11 0.0869 0.117 12 11 0.0911 0.117

13 12 0.1406 0.134 13 12 0.143 0.134

14 13 0.1945 0.152 14 13 0.1966 0.152

15 14 0.2484 0.171 15 14 0.2504 0.171

16 15 0.3024 0.19 16 15 0.3043 0.19

17 16 0.3563 0.21 17 16 0.3582 0.21

18 17 0.4107 0.231 18 17 0.4139 0.231

19 18 0.4644 0.252 19 18 0.4689 0.252

20 19 0.5178 0.274 20 19 0.5232 0.274

21 20 0.5708 0.297 21 20 0.577 0.297

22 21 0.6232 0.32 22 21 0.6305 0.32

23 22 0.6755 0.344 23 22 0.6839 0.344

24 23 0.7283 0.369 24 23 0.7373 0.369

25 24 0.7809 0.394 25 24 0.7902 0.394

26 25 0.834 0.42 26 25 0.8432 0.42

27 26 0.8873 0.445 27 26 0.8963 0.446

28 27 0.9407 0.473 28 27 0.9496 0.473

51

29 30 0.915 0.57 29 30 0.915 0.57

30 35 1.02 0.745 30 35 1.02 0.745

31 40 1.075 0.92 31 40 1.075 0.92

32 45 1.085 1.075 32 45 1.085 1.075

33 50 1.04 1.215 33 50 1.04 1.215

34 55 0.965 1.345 34 55 0.965 1.345

35 60 0.875 1.47 35 60 0.875 1.47

36 65 0.765 1.575 36 65 0.765 1.575

37 70 0.65 1.665 37 70 0.65 1.665

38 75 0.515 1.735 38 75 0.515 1.735

39 80 0.37 1.78 39 80 0.37 1.78

40 85 0.22 1.8 40 85 0.22 1.8

41 90 0.07 1.8 41 90 0.07 1.8

42 95 -0.07 1.78 42 95 -0.07 1.78

43 100 -0.22 1.75 43 100 -0.22 1.75

44 105 -0.37 1.7 44 105 -0.37 1.7

45 110 -0.51 1.635 45 110 -0.51 1.635

46 115 -0.625 1.555 46 115 -0.625 1.555

47 120 -0.735 1.465 47 120 -0.735 1.465

48 125 -0.84 1.35 48 125 -0.84 1.35

49 130 -0.91 1.225 49 130 -0.91 1.225

50 135 -0.945 1.085 50 135 -0.945 1.085

51 140 -0.945 0.925 51 140 -0.945 0.925

52 145 -0.91 0.755 52 145 -0.91 0.755

53 150 -0.85 0.575 53 150 -0.85 0.575

54 155 -0.74 0.42 54 155 -0.74 0.42

55 160 -0.66 0.32 55 160 -0.66 0.32

56 165 -0.675 0.23 56 165 -0.975 0.23

57 170 -0.85 0.14 57 170 -0.85 0.14

58 175 -0.69 0.055 58 175 -0.69 0.055

59 180 0 0.025 59 180 0 0.025

Re 160000 Re 360000


1 0 0 0.0103 1 0 0 0.0079

2 1 0.11 0.0104 2 1 0.11 0.008

3 2 0.22 0.0108 3 2 0.22 0.0084

4 3 0.33 0.0114 4 3 0.33 0.0089

5 4 0.44 0.0124 5 4 0.44 0.0098

6 5 0.55 0.014 6 5 0.55 0.0113

7 6 0.66 0.0152 7 6 0.66 0.0125

8 7 0.746 0.017 8 7 0.77 0.0135

9 8 0.8274 0.0185 9 8 0.8542 0.0153

10 9 0.8527 0.0203 10 9 0.9352 0.0167

11 10 0.1325 0.0188 11 10 0.9811 0.0184

12 11 0.195 0.076 12 11 0.9132 0.0204

13 12 0.1533 0.0134 13 12 0.4832 0.0217

14 13 0.203 0.152 14 13 0.2759 0.0222

52

15 14 0.2546 0.171 15 14 0.2893 0.106

16 15 0.3082 0.19 16 15 0.3306 0.19

17 16 0.362 0.21 17 16 0.3792 0.21

18 17 0.42 0.231 18 17 0.4455 0.231

19 18 0.4768 0.252 19 18 0.5047 0.252

20 19 0.5322 0.274 20 19 0.5591 0.274

21 20 0.587 0.297 21 20 0.612 0.297

22 21 0.6414 0.32 22 21 0.6643 0.32

23 22 0.6956 0.344 23 22 0.7179 0.344

24 23 0.7497 0.369 24 23 0.7715 0.369

25 24 0.8034 0.394 25 24 0.8246 0.394

26 25 0.8572 0.42 26 25 0.878 0.42

27 26 0.9109 0.446 27 26 0.9313 0.446

28 27 0.9646 0.473 28 27 0.9846 0.473

29 30 0.915 0.57 29 30 0.915 0.57

30 35 1.02 0.745 30 35 1.02 0.745

31 40 1.075 0.92 31 40 1.075 0.92

32 45 1.085 1.075 32 45 1.085 1.075

33 50 1.04 1.215 33 50 1.04 1.215

34 55 0.965 1.345 34 55 0.965 1.345

35 60 0.875 1.47 35 60 0.875 1.47

36 65 0.765 1.575 36 65 0.765 1.575

37 70 0.65 1.665 37 70 0.65 1.665

38 75 0.515 1.735 38 75 0.515 1.735

39 80 0.37 1.78 39 80 0.37 1.78

40 85 0.22 1.8 40 85 0.22 1.8

41 90 0.07 1.8 41 90 0.07 1.8

42 95 -0.07 1.78 42 95 -0.07 1.78

43 100 -0.22 1.75 43 100 -0.22 1.75

44 105 -0.37 1.7 44 105 -0.37 1.7

45 110 -0.51 1.635 45 110 -0.51 1.635

46 115 -0.625 1.555 46 115 -0.625 1.555

47 120 -0.735 1.465 47 120 -0.735 1.465

48 125 -0.84 1.35 48 125 -0.84 1.35

49 130 -0.91 1.225 49 130 -0.91 1.225

50 135 -0.945 1.085 50 135 -0.945 1.085

51 140 -0.945 0.925 51 140 -0.945 0.925

52 145 -0.91 0.755 52 145 -0.91 0.755

53 150 -0.85 0.575 53 150 -0.85 0.575

54 155 -0.74 0.42 54 155 -0.74 0.42

55 160 -0.66 0.32 55 160 -0.66 0.32

56 165 -0.675 0.23 56 165 -0.675 0.23

57 170 -0.85 0.14 57 170 -0.85 0.14

58 175 -0.69 0.055 58 175 -0.69 0.055

59 180 0 0.025 59 180 0 0.025

Re 700000 Re 1000000


53

1 0 0 0.0067 1 0 0 0.0065

2 1 0.11 0.0068 2 1 0.11 0.0066

3 2 0.22 0.007 3 2 0.22 0.0068

4 3 0.33 0.0075 4 3 0.33 0.0071

5 4 0.44 0.0083 5 4 0.44 0.0078

6 5 0.55 0.0097 6 5 0.55 0.0091

7 6 0.66 0.0108 7 6 0.66 0.0101

8 7 0.77 0.0118 8 7 0.77 0.011

9 8 0.88 0.0128 9 8 0.88 0.0119

10 9 0.9598 0.0144 10 9 0.9661 0.0134

11 10 1.0343 0.0159 11 10 1.0512 0.0147

12 11 1.0749 0.0175 12 11 1.1097 0.0162

13 12 1.039 0.0195 13 12 1.1212 0.018

14 13 0.8737 0.0216 14 13 1.0487 0.02

15 14 0.6284 0.0236 15 14 0.8846 0.0222

16 15 0.4907 0.117 16 15 0.7108 0.0245

17 16 0.4696 0.21 17 16 0.606 0.128

18 17 0.5195 0.23 18 17 0.5906 0.231

19 18 0.5584 0.252 19 18 0.603 0.252

20 19 0.6032 0.274 20 19 0.6334 0.274

21 20 0.6474 0.297 21 20 0.6716 0.297

22 21 0.6949 0.32 22 21 0.7162 0.32

23 22 0.7446 0.344 23 22 0.7613 0.344

24 23 0.7948 0.369 24 23 0.8097 0.369

25 24 0.8462 0.394 25 24 0.8589 0.394

26 25 0.8984 0.42 26 25 0.9093 0.42

27 26 0.9506 0.446 27 26 0.9618 0.446

28 27 1.0029 0.473 28 27 1.0144 0.473

29 30 0.915 0.57 29 30 0.915 0.57

30 35 1.02 0.745 30 35 1.02 0.745

31 40 1.075 0.92 31 40 1.075 0.92

32 45 1.085 1.075 32 45 1.085 1.075

33 50 1.04 1.215 33 50 1.04 1.215

34 55 0.965 1.345 34 55 0.965 1.345

35 60 0.875 1.47 35 60 0.875 1.47

36 65 0.765 1.575 36 65 0.765 1.575

37 70 0.65 1.665 37 70 0.65 1.665

38 75 0.515 1.735 38 75 0.515 1.735

39 80 0.37 1.78 39 80 0.37 1.78

40 85 0.22 1.8 40 85 0.22 1.8

41 90 0.07 1.8 41 90 0.07 1.8

42 95 -0.07 1.78 42 95 -0.07 1.78

43 100 -0.22 1.75 43 100 -0.22 1.75

44 105 -0.37 1.7 44 105 -0.37 1.7

45 110 -0.51 1.635 45 110 -0.51 1.635

46 115 -0.625 1.555 46 115 -0.625 1.555

47 120 -0.735 1.465 47 120 -0.735 1.465

48 125 -0.84 1.35 48 125 -0.84 1.35

49 130 -0.91 1.225 49 130 -0.91 1.225

50 135 -0.945 1.085 50 135 -0.945 1.085

54

51 140 -0.945 0.925 51 140 -0.945 0.925

52 145 -0.91 0.755 52 145 -0.91 0.755

53 150 -0.85 0.575 53 150 -0.85 0.575

54 155 -0.74 0.42 54 155 -0.74 0.42

55 160 -0.66 0.32 55 160 -0.66 0.32

56 165 -0.675 0.23 56 165 -0.675 0.23

57 170 -0.85 0.14 57 170 -0.85 0.14

58 175 -0.69 0.055 58 175 -0.69 0.055

59 180 0 0.025 59 180 0 0.025

Re 2000000 Re 5000000


1 0 0 0.0064 1 0 0 0.0064

2 1 0.11 0.0064 2 1 0.11 0.0064

3 2 0.22 0.0066 3 2 0.22 0.0066

4 3 0.33 0.0069 4 3 0.33 0.0068

5 4 0.44 0.0073 5 4 0.44 0.0072

6 5 0.55 0.0081 6 5 0.55 0.0076

7 6 0.66 0.009 7 6 0.66 0.0081

8 7 0.77 0.0097 8 7 0.77 0.0086

9 8 0.88 0.0105 9 8 0.88 0.0092

10 9 0.99 0.0113 10 9 0.99 0.0098

11 10 1.0727 0.0128 11 10 1.1 0.0106

12 11 1.1539 0.014 12 11 1.1842 0.0118

13 12 1.2072 0.0155 13 12 1.3673 0.013

14 13 1.2169 0.0172 14 13 1.3242 0.0143

15 14 1.1614 0.0191 15 14 1.3423 0.0159

16 15 1.0478 0.0213 16 15 1.3093 0.0177

17 16 0.826 0.0237 17 16 1.2195 0.0198

18 17 0.7826 0.139 18 17 1.0365 0.0229

19 18 0.7163 0.252 19 18 0.9054 0.148

20 19 0.7091 0.274 20 19 0.8412 0.274

21 20 0.7269 0.297 21 20 0.8233 0.297

22 21 0.7595 0.32 22 21 0.8327 0.32

23 22 0.7981 0.344 23 22 0.8563 0.344

24 23 0.8429 0.369 24 23 0.8903 0.369

25 24 0.8882 0.394 25 24 0.9295 0.394

26 25 0.9352 0.42 26 25 0.9718 0.42

27 26 0.9842 0.446 27 26 1.1093 0.446

28 27 1.0355 0.473 28 27 1.068 0.473

29 30 0.915 0.57 29 30 0.915 0.57

30 35 1.02 0.745 30 35 1.02 0.745

31 40 1.075 0.92 31 40 1.075 0.92

32 45 1.085 1.075 32 45 1.088 1.075

33 50 1.04 1.215 33 50 1.04 1.215

34 55 0.965 1.345 34 55 0.965 1.345

35 60 0.875 1.47 35 60 0.875 1.47

36 65 0.765 1.575 36 65 0.765 1.575

55

37 70 0.65 1.665 37 70 0.65 1.665

38 75 0.515 1.735 38 75 0.515 1.735

39 80 0.37 1.78 39 80 0.37 1.78

40 85 0.22 1.8 40 85 0.22 1.8

41 90 0.07 1.8 41 90 0.07 1.8

42 95 -0.07 1.78 42 95 -0.07 1.78

43 100 -0.22 1.75 43 100 0.22 1.75

44 105 -0.37 1.7 44 105 0.37 1.7

45 110 -0.51 1.635 45 110 0.51 1.635

46 115 -0.625 1.555 46 115 0.625 1.555

47 120 -0.735 1.465 47 120 0.735 1.465

48 125 -0.84 1.35 48 125 -0.84 1.35

49 130 -0.91 1.225 49 130 -0.91 1.225

50 135 -0.945 1.085 50 135 -0.945 1.085

51 140 -0.945 0.925 51 140 -0.945 0.925

52 145 -0.91 0.755 52 145 -0.91 0.755

53 150 -0.85 0.575 53 150 -0.85 0.575

54 155 -0.74 0.42 54 155 -0.74 0.42

55 160 -0.66 0.32 55 160 -0.66 0.32

56 165 -0.675 0.23 56 165 -0.675 0.23

57 170 -0.85 0.14 57 170 -0.85 0.14

58 175 -0.69 0.055 58 175 -0.69 0.055

59 180 0 0.025 59 180 0 0.025

56

APPENDIX B – MODEL RESULTS (NUMERICAL) FOR PITCH ANGLES AT

VARIOUS TSR The results from the Excel model are shown in the following tables. The tables provide F1, average F1, torques and average torques, along with other information. The results are shown for all pitch angles between 80˚ and 107˚ for selected TSR between 0.25 and 7. NACA 0012 summary

Ref # Blade Pitch Average F1 Max F1 Min F1 Average Torque Max Torque Min Torque

1 80 0.23 0.55 -0.06 0.18 0.44 -0.04

2 85 0.30 0.68 -0.07 0.24 0.55 -0.06

3 88 0.41 0.72 0.24 0.33 0.58 0.19

4 90 0.35 0.77 0.06 0.28 0.62 0.05

5 92 0.46 0.77 0.09 0.37 0.62 0.07

6 95 0.40 0.86 0.11 0.32 0.69 0.09

7 100 0.44 0.91 0.11 0.35 0.73 0.09

8 102 0.58 0.88 0.32 0.46 0.70 0.25

9 105 0.52 0.96 0.09 0.41 0.77 0.07

10 107 0.66 0.94 0.33 0.53 0.75 0.26

U 6 m/s

TSR 0.25

chord length 0.070 m

blade length 1.6 m

NACA 0012 summary


1 80 -0.13 0.41 -0.65 -0.11 0.33 -0.52

2 85 0.05 0.90 -0.64 0.04 0.72 -0.51

3 88 0.13 0.73 -0.47 0.10 0.59 -0.38

4 90 0.08 0.59 -0.46 0.06 0.47 -0.37

5 92 0.09 0.71 -0.48 0.07 0.57 -0.38

6 95 0.14 0.88 -0.28 0.12 0.71 -0.22

7 100 0.23 1.15 -0.35 0.19 0.92 -0.28

8 102 0.33 1.18 -0.40 0.26 0.95 -0.32

9 105 0.45 1.49 -0.28 0.36 1.19 -0.22

10 107 0.53 1.42 -0.36 0.43 1.14 -0.29

U 6 m/s

TSR 0.75

chord length 0.07 m

blade length 1.6 m

57

NACA 0012 summary


1 80 -0.42 0.29 -1.22 -0.34 0.23 -0.98

2 85 -0.32 0.35 -1.03 -0.26 0.28 -0.83

3 88 -0.24 0.50 -0.88 -0.19 0.40 -0.71

4 90 -0.30 0.37 -0.89 -0.24 0.30 -0.71

5 92 0.01 0.89 -0.55 0.01 0.71 -0.44

6 95 -0.25 0.44 -0.86 -0.20 0.35 -0.69

7 100 -0.13 0.65 -0.84 -0.11 0.52 -0.67

8 102 0.40 1.29 -0.49 0.32 1.04 -0.40

9 105 0.11 0.88 -0.79 0.08 0.70 -0.63

10 107 0.73 1.62 -0.44 0.59 1.30 -0.35

U 6 m/s

TSR 1

chord length 0.07 m

blade length 1.6 m

NACA 0012 summary


1 80 -0.43 0.98 -2.41 -0.35 0.78 -1.93

2 85 -0.41 1.24 -2.09 -0.33 0.99 -1.68

3 88 -0.40 1.41 -1.58 -0.32 1.13 -1.27

4 90 -0.47 1.28 -1.60 -0.38 1.03 -1.28

5 92 -0.29 1.91 -1.51 -0.23 1.53 -1.21

6 95 -0.42 1.25 -1.50 -0.34 1.00 -1.20

7 100 -0.30 0.97 -1.23 -0.24 0.78 -0.99

8 102 0.01 0.89 -0.91 0.01 0.72 -0.73

9 105 0.15 1.19 -1.21 0.12 0.96 -0.97

10 107 0.54 1.10 -0.64 0.43 0.88 -0.51

U 6 m/s

TSR 1.5

chord length 0.07 m

blade length 1.6 m

58

NACA 0012 summary


1 80 -0.39 3.67 -1.78 -0.31 2.94 -1.43

2 85 -0.62 0.75 -3.47 -0.50 0.60 -2.78

3 88 -0.49 1.62 -3.33 -0.39 1.30 -2.67

4 90 -0.38 2.56 -2.96 -0.31 2.05 -2.38

5 92 -0.59 2.20 -2.43 -0.47 1.76 -1.95

6 95 -0.29 3.30 -2.35 -0.23 2.65 -1.88

7 100 -0.63 1.67 -1.56 -0.50 1.34 -1.25

8 102 -0.51 1.12 -1.92 -0.41 0.90 -1.54

9 105 0.06 2.02 -2.16 0.05 1.62 -1.73

10 107 0.18 1.66 -1.26 0.14 1.33 -1.01

U 6 m/s

TSR 2

chord length 0.07 m

blade length 1.6 m

NACA 0012 summary


1 80 -0.10 3.43 -2.09 -0.08 2.75 -1.68

2 85 -0.90 0.93 -2.74 -0.72 0.74 -2.19

3 88 -1.11 0.94 -4.09 -0.89 0.76 -3.27

4 90 -0.87 1.88 -3.85 -0.70 1.50 -3.08

5 92 -0.50 2.93 -3.49 -0.40 2.35 -2.80

6 95 -0.52 3.26 -2.43 -0.41 2.61 -1.95

7 100 -1.12 0.85 -2.70 -0.90 0.68 -2.16

8 102 -0.85 2.17 -2.03 -0.68 1.74 -1.62

9 105 -0.29 2.33 -2.32 -0.23 1.86 -1.86

10 107 0.06 2.30 -1.26 0.04 1.84 -1.01

U 6 m/s

TSR 2.25

chord length 0.07 m

blade length 1.6 m

59

NACA 0012 summary


1 80 3.42 8.03 0.74 2.74 6.43 0.59

2 85 0.02 7.25 -3.54 0.02 5.81 -2.83

3 88 -1.24 1.35 -3.73 -1.00 1.08 -2.99

4 90 -1.78 3.06 -6.33 -1.42 2.45 -5.07

5 92 -2.10 1.40 -6.23 -1.69 1.12 -4.99

6 95 -1.91 3.30 -6.14 -1.53 2.64 -4.92

7 100 -1.78 2.52 -3.17 -1.43 2.02 -2.54

8 102 -2.42 0.20 -4.62 -1.94 0.16 -3.70

9 105 -1.07 2.28 -2.64 -0.86 1.82 -2.11

10 107 -0.83 1.62 -3.84 -0.67 1.30 -3.08

U 6 m/s

TSR 3

chord length 0.07 m

blade length 1.6 m

NACA 0012 summary


1 80 3.32 10.08 -0.12 2.66 8.08 -0.10

2 85 1.93 6.74 -0.72 1.55 5.40 -0.58

3 88 -0.87 4.76 -5.23 -0.70 3.82 -4.19

4 90 -0.58 3.31 -5.18 -0.46 2.66 -4.15

5 92 -0.37 5.85 -8.44 -0.29 4.68 -6.76

6 95 -0.74 3.85 -7.32 -0.59 3.08 -5.87

7 100 -2.04 7.60 -5.71 -1.63 6.09 -4.58

8 102 -2.07 5.65 -3.62 -1.66 4.52 -2.90

9 105 -2.62 0.55 -5.54 -2.10 0.44 -4.44

10 107 -1.15 3.20 -3.40 -0.92 2.56 -2.73

U 6 m/s

TSR 3.5

chord length 0.07 m

blade length 1.6 m

60

NACA 0012 summary


1 80 3.37 9.93 -0.71 2.70 7.96 -0.57

2 85 5.78 9.15 4.62 4.63 7.33 3.70

3 88 5.73 12.26 -2.20 4.59 9.82 -1.76

4 90 3.27 16.84 -6.93 2.62 13.49 -5.55

5 92 1.33 8.99 -6.24 1.07 7.20 -5.00

6 95 -0.47 6.71 -8.65 -0.37 5.38 -6.93

7 100 -3.24 8.02 -8.81 -2.59 6.42 -7.06

8 102 -3.99 5.02 -6.59 -3.20 4.02 -5.28

9 105 -1.91 -1.50 -2.66 -1.53 -1.20 -2.13

10 107 -1.88 2.42 -6.71 -1.51 1.94 -5.37

U 6 m/s

TSR 4

chord length 0.07 m

blade length 1.6 m

NACA 0012 summary


1 80 3.74 10.98 -0.85 2.99 8.80 -0.68

2 85 4.92 8.92 3.09 3.94 7.15 2.48

3 88 10.27 11.66 0.35 8.23 9.34 0.28

4 90 10.02 17.93 0.99 8.03 14.36 0.79

5 92 6.07 20.80 -8.45 4.87 16.66 -6.77

6 95 0.57 7.34 -6.10 0.46 5.88 -4.88

7 100 -4.63 8.16 -12.22 -3.71 6.54 -9.79

8 102 -6.22 4.29 -9.67 -4.98 3.44 -7.74

9 105 -4.52 -4.25 -5.55 -3.62 -3.41 -4.44

10 107 -0.28 0.21 -1.96 -0.23 0.17 -1.57

U 6 m/s

TSR 4.5

chord length 0.07 m

blade length 1.6 m

61

NACA 0012 summary


1 80 4.80 12.49 -0.73 3.85 10.01 -0.58

2 85 3.84 7.82 2.13 3.08 6.26 1.71

3 88 10.54 11.99 9.71 8.44 9.60 7.78

4 90 16.29 18.18 15.16 13.05 14.57 12.14

5 92 15.23 25.19 6.50 12.20 20.18 5.21

6 95 4.64 13.18 -6.19 3.72 10.56 -4.96

7 100 -6.30 8.30 -15.83 -5.05 6.65 -12.68

8 102 -9.02 3.54 -13.19 -7.22 2.83 -10.57

9 105 -7.45 -6.95 -7.97 -5.97 -5.57 -6.39

10 107 -2.52 -2.03 -3.57 -2.02 -1.63 -2.86

U 6 m/s

TSR 5

chord length 0.07 m

blade length 1.6 m

NACA 0012 summary


1 80 6.65 14.62 3.41 5.33 11.71 2.73

2 85 2.93 7.17 1.05 2.35 5.74 0.84

3 88 9.87 11.44 8.69 7.91 9.16 6.96

4 90 17.50 18.83 16.63 14.02 15.09 13.32

5 92 20.79 27.74 15.15 16.66 22.23 12.13

6 95 10.08 20.60 -3.62 8.08 16.50 -2.90

7 100 -5.99 8.12 -19.78 -4.80 6.50 -15.84

8 102 -11.25 2.30 -17.08 -9.02 1.84 -13.68

9 105 -10.80 -10.37 -11.45 -8.65 -8.31 -9.17

10 107 -5.22 -4.73 -6.50 -4.18 -3.79 -5.21

U 6 m/s

TSR 5.5

chord length 0.07 m

blade length 1.6 m

62

NACA 0012 summary


1 80 8.99 17.20 5.71 7.20 13.78 4.57

2 85 2.20 6.44 0.55 1.76 5.16 0.44

3 88 9.03 10.43 8.19 7.23 8.36 6.56

4 90 17.64 18.86 16.78 14.13 15.11 13.44

5 92 26.85 29.77 24.31 21.51 23.85 19.47

6 95 17.61 27.08 5.87 14.11 21.69 4.71

7 100 -5.55 8.04 -16.23 -4.45 6.44 -13.01

8 102 -12.97 1.05 -21.50 -10.39 0.84 -17.23

9 105 -14.53 -13.97 -15.26 -11.64 -11.20 -12.23

10 107 -8.34 -7.79 -9.79 -6.68 -6.24 -7.84

U 6 m/s

TSR 6

chord length 0.07 m

blade length 1.6 m

NACA 0012 summary


1 80 11.75 19.96 7.76 9.41 15.99 6.22

2 85 1.40 6.72 -0.36 1.12 5.38 -0.29

3 88 7.78 10.42 6.94 6.23 8.34 5.56

4 90 17.22 19.00 16.20 13.79 15.22 12.98

5 92 29.48 31.47 27.43 23.61 25.21 21.97

6 95 28.11 34.36 12.39 22.52 27.52 9.93

7 100 -5.56 8.18 -18.19 -4.46 6.55 -14.57

8 102 -15.34 -0.19 -26.26 -12.29 -0.15 -21.04

9 105 -18.61 -18.12 -19.62 -14.91 -14.52 -15.72

10 107 -11.79 -11.33 -13.44 -9.45 -9.07 -10.77

U 6 m/s

TSR 6.5

chord length 0.07 m

blade length 1.6 m

63

NACA 0012 summary


1 80 15.01 23.82 11.63 12.03 19.08 9.31

2 85 0.89 6.02 -1.27 0.71 4.82 -1.01

3 88 6.92 8.72 5.47 5.54 6.99 4.38

4 90 17.07 17.65 16.40 13.68 14.14 13.14

5 92 30.92 32.42 28.96 24.77 25.97 23.20

6 95 35.86 48.95 23.25 28.73 39.22 18.63

7 100 -5.53 7.42 -17.80 -4.43 5.94 -14.26

8 102 -18.84 -1.72 -31.27 -15.09 -1.38 -25.05

9 105 -23.06 -22.39 -23.94 -18.47 -17.93 -19.18

10 107 -15.58 -15.01 -17.23 -12.48 -12.03 -13.80

U 6 m/s

TSR 7

chord length 0.07 m

blade length 1.6 m

64

APPENDIX C – MATLAB PROGRAMMING CODE FOR ANALYSIS MODEL The following MATLAB codes were used to calculate the angles of attack (rad) and the magnitudes of the relative wind speeds (m/s), respectively. Code to Calculate Angle of Attack, Alpha (radians)

outfile = fopen('angles.txt', 'r'); us = input('Enter the free stream velocity, U '); tsr = input('Enter the tip speed ratio, tsr '); n = 0; fprintf(outfile,'Alpha\n'); while n <= 360 theta = n*pi/180; U = [us, 0]; V = [tsr*us*cos(theta), tsr*us*sin(theta)]; W = [U(1,1)+V(1,1), U(1,2)+V(1,2)]; Vmag = sqrt(V(1,1)^2+V(1,2)^2); Wmag = sqrt(W(1,1)^2+W(1,2)^2); dp = dot(V,W); a = acos(dp/(Vmag*Wmag)); alpha = a*180/pi; fprintf(outfile,'% .2d\n', n,alpha); n = n+5; end

65

Code to Calculate Relative Wind Speed, W (m/s)

outfile = fopen('W.txt', 'r'); us = input('Enter the free stream velocity, U '); tsr = input('Enter the tip speed ratio, tsr '); n = 0; fprintf(outfile,'Relative Wind Speed\n'); while n <= 360 theta = n*pi/180; U = [us, 0]; V = [tsr*us*cos(theta), tsr*us*sin(theta)]; W = [U(1,1)+V(1,1), U(1,2)+V(1,2)]; Vmag = sqrt(V(1,1)^2+V(1,2)^2); Wmag = sqrt(W(1,1)^2+W(1,2)^2); dp = dot(V,W); a = acos(dp/(Vmag*Wmag)); alpha = a*180/pi; fprintf(outfile,'% .2d\n', n,W); n = n+5; end

66

APPENDIX D – SOLID EDGE DRAWINGS

76

APPENDIX E – GANTT CHART

Vertical Axis Wind Turbine

Documents

Transcript of Vertical Axis Wind Turbine