wind turbines introduction

7/29/2019 Wind Turbines Introduction

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Wind Turbines

1



Wind Energy - Wind Power

A moving air with velocity of has a kinetic energy of

If the moving air has a density , then the kinetic

energy per volume of air becomes:

V

][2

1 2 J mV E

][2

13

2

m J V E V

2



The Energy Extracting Stream-tube of a Wind Turbine

The volume flow rate per second through A is:

][3

S m AV V

3



Power = Energy per Second

Power = Energy per Volume x Volume per second

Combining the above equations gives:

AV V Pair 2

2

1

][2

1 3 W AV Pair

4



From the above derived equation:

• The power is proportional to the density . Density

varies with height and temperature

• In case of horizontal axis windmills the power is

proportional to the area (area swept by the blades)

and thus to R2.

• The power varies with the cube of the undisturbed

wind velocity . Note that the power increases eightfold

if the wind speed doubles.

5



Maximum Power Coefficient

• The actual power extracted by the rotor blades is the

difference between upstream and downstream

powers.

• The maximum power extraction is reached when

the wind downstream is 1/3 of the undisturbed upstream velocity .

6



The axial Stream tube model

22

.2

1oextr V V rate flowmassP

7



2

oV V Arate flowmass

22

max22

1o

o V V V V

AP

2

2max

323

21 V V

V V

AP

93

2

2

12

2

.max

V V

V AP

3

.max2

1

27

16

AV P

8



Classification of Windmill Rotors

Horizontal Axis Rotors

Horizontal axis wind turbines (HAWT) have

their axis of rotation horizontal to the ground

and almost parallel to the wind stream. Most

of the commercial wind turbines fall under

this category.

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Advantages of horizontal axis wind turbines are:

• Low cut-in wind speed and easy furling

• They show relatively higher power coefficient

Disadvantage of horizontal axis wind turbines are:

• Generator and gearbox are to be placed over the tower

making its design more complex and expensive

• They need for tail or yaw drive to orient the turbine

towards wind.10



Depending on the number of blades, HAWTs are classified

as single bladed, two bladed, three bladed and multi

bladed.

11



Vertical Axis Rotor

The axis of rotation of vertical axis windmill is vertical to

the ground and almost perpendicular to the wind

direction.

The advantages of these windmills are:

• They can receive wind from any direction.

• Complicated yaw devices are not needed

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• Generator and gearbox of such systems can be housed

at the ground level which makes the tower design

simple and more economical

• Maintenance of these windmills can be done at the

ground level

The major disadvantage of these systems is that they

are not self starting.

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The Rotor

The windmill rotates because of forces acting on the

blades.

The cross sections of these blades have several forms.

Air flow over blades (airfoil) results two forces, Lift and

Drag.

Lift is the force measured perpendicular to the airflow

and drag is measured parallel to the flow

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Lift and Drag

• The lift force result in a force working in tangential

direction at some distance from the rotor center.

• This force is diminished by the component of the drag

in the tangential direction.

15



Lift and Drag forces

16



The product of the net tangential force multiplied by

the corresponding distance from the rotor center gives

the contribution of the blade element to the torque Q

of the rotor.

The rotor rotates at angular speed ,

srad n 2

17



The power such a rotor extracts from the wind is

transformed to mechanical power.

This power is equal to the product of the torque and

the angular speed.

W QP

18



Rotor Blade Design

The windmill rotates because of forces acting on the

blades.

The cross sections of these blades have several forms.

Air flow over blades (airfoil) results two forces, Lift and

Drag.

Lift is the force measured perpendicular to the airflow

and drag is measured parallel to the flow

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Lift and Drag

• Chord line: - it connects the leading edge and the

trailing edge of the airfoil.

• Angle of attack: - an angle between the chord line and

the direction of the airflow.

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To describe the performance of an airfoil independent

of size and velocity, Lift L and drag D are divided by

where, AV 2

2

1

3m

kg Density Air s

mVelocityFlowV

2)( m Length Bladechord Area Blade A

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The results of these divisions are called lift coefficient

and drag coefficient .

The amount of lift and drag depends on the angle of

attack. This dependence is a given characteristic of an

airfoil is always presented in and graphs.

lC

d C

AV

LC l 2

2

1

AV

DC d 2

2

1

lC d

C

22



For the design of a windmill it is important to find from

such graphs the and values that correspond with a

minimum ratio.

lC

l

d

C

C

23



Drag lift ratio, angle of attack and lift coefficient

for different airfoils

24



The mechanical power can be expressed as the power

in air multiplied by a factor .

is called power coefficient and is a measure for the

success we have in extracting power from the wind.

PC

air pmech PC P

PC

23

21 RV

PC mechP

25



The local speed ratio is the speed U of the rotor at

radius r by the wind speed.

The speed-ratio of the element of the rotor blade at

radius R is called tip-speed ratio:

V

r

V

ur

V

Ro

26



Calculation of blade chords and blade setting

• Design of the rotor consists in finding both values of

the chord and the setting angle ,

• The setting angle is the angle between the chord and

the plane of rotation.

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The following parameters must be found before

making the calculation of the chords and the setting

angles:

Rotor R: the radius: the design tip speed ratio

B: number of blades

Airfoil : design lift coefficient

: Corresponding angle of attack

d

ld C

d

28



The choice of and B are more or less related as the

following table suggests.

d

B 1 6 – 20 2 4 – 12 3 3 – 6 4 2 – 4 5-8 2 – 3 8-15 1 - 2

d

29



The type of load determines :

• Water pumping windmills driving piston pumps have 1 < < 2.

• Electricity generating wind turbines usually have 4 < < 10.

The radius of a rotor can be fixed by a formula,

Where: can be approximated to be equal to 0.1 for wind

pump and it could be changed to 0.15 to 0.2 for electric

generators.

d

d

d

3

21

V C

P R

p

pC 2

1

30



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The airfoil data are selected from Table 1. Four

formulas describe the required information about ,

and C.

Chord:

Blade setting angle:

Flow angle:

Design Speed:

r ld BC

r C

cos1

8

r r

r

r

1arctan

3

2

R

r d r

32



Example: Find the chord C and setting angle of the blade

for a curved plate profile (10 % curvature) with the

given parameters:

2

6

37.1

d

B

m R

Rotor

o

d

lC Airfoil

4

1.1

33



Soln.

To keep the lift coefficient at a constant value of , a

varying chord C and varying setting angle will result.

To keep the blade with a constant chord (for ease of

production) then the lift coefficient will vary along the

blade.

ld C

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Constant Lift Coefficient

By dividing the radius of the rotor at four points andapplying the above formulas the following values are

found

position r/R r(m) C (m) 1 0.25 0.34 0.5 42.3o 4 o 38.3 o 0.337 2 0.5 0.68 1 30.0 o 4 o 26.0 o 0.347 3 0.75 1.03 1.5 22.5 o 4 o 18.5 o 0.298 4 1 1.37 2 17.7 o 4 o 13.7 o 0.247

r r d

35



The figure below shows the chord of the blade at the

four division points.

36



Constant Chord

• The constant lift coefficient approach has a difficulty of

manufacturing as the twist varies discontinuously along

the blade. To avoid that a constant chord approach is

used.

• To have a constant chord the lift coefficient at different

positions along the blade will vary.

r l BC

r C

cos1

8

37



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The angle of attack also varies with variation in lift

coefficient. Therefore graph is needed to determine

values at different positions.

Choosing a chord of 0.324 m and three positions along

the blade, and applying the above formula the following

data are found.

lC

position r(m) C (m) chosen

1 0.5 0.324 0.73 35.9 1.23 6.4 29.5 27 2 0.86 0.324 1.26 25.7 1.10 3.6 22.1 23 3 1.22 0.324 1.78 19.5 0.91 0.2 19.3 19

r

r

lC

39



The blade shape and setting angles of the blade are

shown below.

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wind turbines introduction

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