wind turbine terminologies

7/24/2019 Wind Turbine terminologies

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WIND TURBINE

EXPERIMENTAL ANALYSIS OF WIND TURBINE BLADES AIRFOIL 29

CHAPTER 3.

WIND TURBINE

TERMINOLOGIES

Coefficient of power

Coefficient of power is the most important variable in wind turbine aerodynamics. This

variable is also a means to compare different turbines.

Coefficient of power PC is defined as the ratio power extracted by the turbine rotor

because of axial force acting on the rotor to kinetic power available in the wind.

o

PP

PC

)( 31 XX CCmX

2312 )( XXXX CCCmXCP

)( 312

22 XXX CCCAP

It is convenient to define to define an axial flow induction factor, a (assumed to be

invariant with radius), for the actuator disc or turbine rotor:

1

21 )(

X

XX

C

CCa


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123 2 XXX CCC

And therefore P is given as;

23

12 )1(2 aCAaP X

22

)( 3 12122

1 XXXo

CACACP

2

)1(4 aaP

P

Co

P

The maximum value of PC is found by differentiating PC with respect to a .

0)31)(1(4 aaad

dCP

The above equation gives two roots, a=1/3 and 1.0 . Using the first root, the maximum

value of the coefficient of power is given as

593.027

16max PC

This value of PC is often referred to as Betz lmit, referring to the maximum possible

power coefficient of the turbine.


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The axial force coefficient

The axial force coefficient is defined as

2

2

12

1 AC

XC

X

x


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2

2

1

21

2

1

)(2

AC

CCmC

X

XXx

2

1

212 )(4

X

XXXx

C

CCCC

)1(4 aaCx

we can find the maximum value of xC by differentiating the the above expression for

xC with respect to a and equating it to zero.

084 aad

dCx

This gives the maximum value of xC as unity at a =0.5.

Variation of PC and xC as a function of a (axial induction factor).


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Tip speed ratio

Tip speed ratio is one of the most important non dimensional parameter for the rotors ofHAWTs, and is defined as;

J = speed of the tip of the rotor

Free stream velocity(v)

v

Rn

v

RJ

2

This parameter controls the operating conditions of a turbine and strongly influence the

values of the flow induction factors a and 'a which in turn influence the maximum

possible values of PC . Maximum PC occurs at specific tip speed ratio.

Typically, the values of tip speed ratio lies between 1 to 1.5 for pumping purpose, and

between 6 to 9 for electricity production.


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WIND TURBINE


AERODYNAMIC THEORIES OF WIND TURBINE

The analysis of aerodynamic behavior of wind turbines can be started without any

specific turbine design just by considering the energy extraction process. A simple model,

known as the actuator disc model can be used to calculate the power output of ideal

turbine rotor and the wind thrust on the rotor. Additionally more advanced methods,

including momentum theory, blade element theory and finally blade element momentum

theory are introduced. BEM theory is used to obtain the optimum blade shape and also to

predict the performance parameter of the rotor for ideal, steady operating condition.

Blade element momentum theory combines two methods to analyze the aerodynamic

performance of a wind turbine. These are momentum theory and blade element theory

which are used to outlined the governing equations for aerodynamic design and power

prediction of HAWT rotor. Momentum theory analyses the momentum balance on a

rotating annular stream tube passing through a turbine and blade element theory examines

the forces generated by the airfoil lift and drag coefficient at various sections along the

blade. Combining both theories gives a series of equations that can be solved iteratively.

Actuator disc theory

The analysis of the aerodynamic behavior of the wind turbines can be started without any

specific turbine design just by considering the energy extraction process. The simplest

model of a wind turbine is the so-called actuator disc model, where the turbine is replaced

by a circular disc through which the air stream flows. There are some assumptions

associated with this theory but even though the analysis yields useful approximate results.


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Following are the assumptions:

1. Steady uniform flow upstream of the disc;

2. Uniform and steady velocity at the disc;

3. No flow rotation produced by the disc;

4. The flow passing through the disc is contained both upstream and downstream by the

boundary stream tube;

5. The flow is incompressible.

Because the actuator disc offers a resistance to the flow, the velocity of the air is

reduced as it approaches the disc and there will be a corresponding increase in pressure.

The flow crossing through the disc experiences a sudden drop in pressure below the

ambient pressure. The discontinuity in pressure at the disc characterizes the actuator.

Downstream of the disc there is a gradual recovery of the pressure to the ambient value.

We define the axial velocities of the flow far upstream (x - ), at the disc (x=0) and far

downstream (x ) as 321, XXX andCCC , respectivly. By continuity equation, the mass

flow rate is given as

22ACxm

Where = air density and 2A = area of disc.


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The axial force acting on the disc

)( 31 XX CCmX

And the corresponding power extracted by the turbine or the actuator disc is

2312 )( XXXX CCCmXCP

The rate of energy loss by the wind must then be

2

)( 2 32

1 XXW

CCmP


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WIND TURBINE


Assuming no other losses, we can equate the power lost by the wind to the power gained

by the turbine rotor or actuator

PPW

231

2

3

2

1 )(2

)(XXX

XX CCCmCCm

On simplification we obtain;

2

)( 312

XXX

CCC

)( 312

22 XXX CCCAP

212

222 XXX CCCAP

It is convenient to define to define an axial flow induction factor, a (assumed to be

invariant with radius), for the actuator disc or turbine rotor:

1

21 )(

X

XX

C

CCa

)1(12 aCC XX

23

12 )1(2 aCAaP X


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Momentum theory

Axial force

Consider a stream tube around a wind turbine(represented by disc) as shown in figure.

Three stations are shown in the diagram 1, someway upstream of the turbine 2, at the

plane of disc(wind turbine) 3, someway at the downstream of the turbine. At 2 energy is

extracted from the wind and there is a change in pressure as a result.

The air passing across the disc undergoes an overall change in velocity 31 XX CC and

a corresponding rate of change of momentum equal to the mass flow rate multiplied by

this velocity change. The force causing this momentum change is equal to the difference

in pressure across the disc times the area of the disc. Thus,

312231222 XXXXX CCCACCmApp

31222 XXX CCCppp


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The difference in pressure p is obtained by application of bernoullis equation to the

two flow regimes of the stream tube.

Applying bernoullis equation to the region 1-2;

2

221

2

2

121

1 XX CpCp

And to the region 2-3;

2

22

2

33 2

1

2

1XX CpCp

By taking the difference of two equation, we get ;

222 32 12

1ppCC XX

XAppACC XX 22222 32 121

And using the below equations,

2

)( 312

XXX

CCC

1

21 )(

X

XX

CCCa

We get ;

2

2

1 142

1AaaCX X


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WIND TURBINE


Rotating annular stream tube

It is evident that the torque exerted on the rotor disc by the air passing through it requires

an equal and opposite torque to be exerted on the air. As a consequence, this reaction

torque causes the air leaving the rotor to rotate incrementally in the opposite direction to

that of the rotor. Thus the wake leaving the rotor blades will have a velocity component in

the direction tangential to the blade rotation as well as an axial velocity component.

The flow entering the rotor has no rotational motion at all. The flow exiting the rotor

has rotation and this remain constant as the flow travels downstream. We can define the

change in the tangential velocity in terms of a tangential flow induction factor, 'a .

r

Ca

2' 2


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Consider such an elementary annulus of a HAWT of radius r from the axis of rotation and

of radial thickness dr.

Moment of inertia of an annulus, 2mrI

Angular Moment, IL

Torque,dt

dLT


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22

dt

dm

dtdt

dIT r

mrd

So for a small element the corresponding torque will be:

2rmddT

For a rotating annular element

22 XCrdrmd

222 rCrdrdT X

2

'a

1

21 )(

X

XX

C

CCa

drraaCdT X 31 '14

So momentum theory has yielded equations for axial and tangential forces on an annular

element of fluid.


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WIND TURBINE


Blade element theory

Blade element theory relies on two key assumptions:

1. There is no aerodynamic interaction between different blade elements.

2. The forces on the blade elements are solely determined by the lift and drag coefficients

Consider now a turbine with Z blades of tip radius R each of chord l at radius r and

rotating at angular speed . The pitch angle of the blade at radius r is measured from

the zero lift line to the plane of rotation. The axial velocity of the wind at the blades is the

same as the value determined from actuator disc theory and is perpendicular to the plane

of rotation

Figure shows the blade element moving from right to left together with the velocity

vectors relative to the blade chord line at radius r. The resultant of the relative velocity

immediately upstream of the blades is,


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WIND TURBINE


BLADE DESIGN PROCEDURE

1. Determine the rotor diameter require from site condition.

33

2

1VRCP P

Where ;

P is the power output.

PC is the expected coefficient of performance (0.4 for modern three bladed

wind turbine).

is the expected electrical and mechanical efficiency (0.9 would be a suitable

value).

R is the tip radius.

V is the expected wind velocity.

2. Choose a tip speed ratio for the machine. For water pumping take 1


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WIND TURBINE


6. Choose the design aerodynamic condition for each airfoil. Typically select 80% of

the maximum lift value, this choice effectively fixes the blade twist. On long blades a

very large degree of twist is required to obtain 80% of the maximum lift near the hub.

This is not necessarily desirable as the hub produces only a small amount of power

output , a compromise is to accept that the airfoil will have very large angles of

attack at hub.

7. Choose a chord distribution of the airfoil. There is no easily physical accessible way

of doing this but a simplification of an ideal blade is given by

rB

rc

3

cos8

This gives a moderately complex shape and a linear distribution of chord may be

considered easier to make.

8. Divide the blade into N elements. Typically 10 to 20 elements would be used.

9. As a first guess for the flow solution use the following equations. These are based on

an ideal blade shape derived with the wake rotation, zero drag and tip losses. Note

that these equations provide an initial guess only. The equations are given as follows:

r

1tan

3

290 10

1

'

2

sin

cos41

LCa

1431'

a

aa

10. Calculate rotor performance and then modify the design as necessary. This is an

iterative process.


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A typical experience shows the relation between TSR and number of blades(B).

B

1 8-24

2 6-12

3 3-6

4 3- 4

More than 4 1- 3


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WIND TURBINE


SCALING OF WIND TURBINE

Before manufacturing of actual full scale prototype of a wind turbine , it is required to

perform certain performance tests on a scale model to predict its performance subjected

to certain set to conditions. Such tests are required to compare the actual performance and

anticipated performance.

A number of scaling parameters and geometric parameters are considered during the

design of a scale model of a wind turbine rotor, which also include mass scaling, mach no.

scaling, Reynolds similarity and geometric scaling.

Full scale wind turbine have a Reynold number based on the blade tip speed and tip

chord on the order of 610 . Reynold similarity can not be achieved since it require high

flow velocity which could violate the assumptions of incompressible flow in air.

Thus oftenly only geometric similarity and tip speed ratio matching are employed.

This results in impractical rotational speed. For wind tunnel tests that involve Reynolds

no. less than approximately 500,000 Reynold no. matching is necessary. When including

Reynold no. matching in the scaling process, keeping rotational velocities realistic

become even more challenging and preventing impractical free stream velocities become

difficult.

Sometimes on scaling a turbine for design or wind tunnel testing, typically only

geometric scaling and TSR ( tip speed ratio ) matching is applied.

U

RTSR

For most medium to large turbines (>20m) operate at higher Reynold's number and

matching Reynold number for scaling does not need to be accounted.

cUrel

Re

In case of Reynold number below 500,000 the flow can vary significantly with both flow

and geometric parameters.


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WIND TURBINE


WIND TURBINE SCALING LAWS WHITHOUT

REYNOLD NUMBER MATCHING

QUANTITY SYMBOL RELATIONS SCALE DEPENDENCE

Power P

2

2

1

2

1

R

R

P

P 2R

Torque Q

3

2

1

2

1

R

R

Q

Q 3R

Thrust T

2

2

1

2

1

RR

TT 2R

Rotational

1

2

1

2

1

R

R 1R

Speed

Weight W

3

2

1

2

1

R

R

W

W 3R

Aerodynamic

Moments AM

3

2

1

2

1

R

R

M

M

A

A 3R

Centrifugal

Force CF

2

2

1

2

1

R

R

F

F

C

C 2R


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WIND TURBINE


WIND TURBINE SCALING LAWS WITH

REYNOLD NUMBER MATCHING

PARAMETRS SYMBOL RELATION

Radius R scR

R

2

1

Chord c scc

c

2

1

Kinematic

Viscosity 12

1

Free stream UscU

U 1

2

1

Velocity

Rotational 2

2

1 1

sc

Velocity

Rotor power rotorP

scP

P

rotor

rotor 1

2

1

Torque sc2

1


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WIND TURBINE


HAWT BLADE SECTION CRITERIA

The essential requirements for a wind turbine blades is its aerodynamic performance,structural strength and stiffness, ease of manufacture and maintenance. It was assumed

that blades with high lift and low drag were the best choice for wind turbine blades and

thus the standard aerofoils, e.g., NACA 44XX, NACA 230XX, (where the XX denotes

thickness to chord ratio, as a percentage), that were suitable for aircraft were selected for

wind turbines.

The main factor that influence the liftdrag ratio of a given aerofoil section is the

Reynolds number. Earlier works showed that optimal performance of a turbine blade

depends on the product of blade chord and lift coefficient, LcC . When other turbine

parameters such as the tipspeed ratio J and radius R are kept constant, narrower blades

can be used with high value of LC . It is not necessary that narrower blades are responsible

for lower viscous losses. Reynolds number plays an important role in viscous losses. In

fact lower reynolds number often produces higher values of DC .

Another important factor to consider is the effect on the blade structural stiffness, which

largely depends upon thicness of the blade. The standard aerofoils also suffered from a

serious fault; such as, a gradual degradation of performance due to roughness effects by

contamination on the leading edge. The roughness also degrades the aerofoils lift-curve

slope and increases profile drag, further contributing to losses. Small scale wind turbines

are more prone to losses due to roughness because of their lower elevation that allows the

accretion of more insects and dust particles and the debris.


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WIND TURBINE


PRESSURE DISTRIBUTION MEASUREMENT

Pressure distribution is the variation of static pressure on the surface of a model. Lift on

an airfoil is because of the pressure difference between the upper and lower surface of the

airfoil. A prior knowledge of pressure distribution over the airfoil will give us lift acting

on the airfoil.

Pressure distribution over the airfoil is measured using pressure tapping leading to the

pressure transducers or suitable pressure sensing element like multitube manometer.

Pressure tapping are simply a hole which are perpendicular to the surface of a body. This

holes are connected to pressure sensing elements through tubes. This tubes are of very

small diameter(1mm internal diameter). Earlier the pressure sensing elements were

multitube manometer but now a days piezoelectric pressure sensors are common.

Lift and drag on the airfoil depends upon the quality of pressure measurement. The

pressure tapping should cover the entire airfoil. They should be denser near the leading

and trailing edge.

Pressure sensor connection

Pressure sensor can be connected to pressure tapping in two ways;

1. The pressure sensors are connected to pressure tapping by short tubes, inside the

model and then the sensors are connected to data acquisition system by long electric

cables. Such kind of connection is required for unsteady pressure measurements.

2. The pressure sensors are connected to pressure tapping by long tubes and pressure

sensing element lies outside the model. Such kind of connection is necessary for small

models that can not accommodate the pressure sensors inside.


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WIND TURBINE


Pressure Taping placement

Pressure taping are to be placed on the airfoil in a manner as shown in the figure. A total

of 19 number of taping are to be done on the airfoil. 9 taping on the upper surface and 9

taping on the lower surface. One taping is at the leading edge. Taping placement on all

airfoil are to be done in similar fashion.

All the pressure taping are connected to multitube manometer in a manner as discussed

above. Pressure is taken by reading the column of multitube manometers and thus

pressure distribution is obtained. Coefficient of pressure is calculated at each pressure

taping point and is plotted against chord length at various angle of attack. A typical

coefficient of pressure distribution is shown in the figure.

2

2

1V

ppC iaPi


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WIND TURBINE


Where, ap is static pressure on the surface of airfoil in pascal.

ip is the inlet static pressure or test section static pressure.

V is free stream velocity.

Figure. coefficient of pressure distribution over an airfoil

Coefficient of Lift and drag on the airfoil can also be obtain by pressure distribution.

Coefficient of lift and drag can be given as;

P

LL

AV

FC

2

2

1

P

DD

AV

FC

2

2

1

clAP

Where, LF and DF are the lift and drag forces respectively.

PA is the projected area

c and l are the chord length and span of the airfoil model


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The total drag on the airfoil is sum of frictional drag and pressure drag(form drag).

Lift on an airfoil is because of the pressure difference between the upper and lower

surface of the airfoil. A

Coefficient of lift and drag can also given as ;

sincos XZL CCC

cossin XZD CCC


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Where, XC and ZC are the coefficient of resolved forces of resultant force along X

and Z direction.

is the angle of attack

surface

PXc

xdCC

surafce

PZc

zdCC

ZC and XC can also be obtained by numerical integration

xCC PijZ2

1

zCC PijX 21

ij xxx

ij zzz


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WIND TURBINE

is measured from the leading edge in a direction parallel to chord line.

z is measured from the chord line in a direction perpendicular to chord line.

PijC is pressure coefficient acting on the airfoil between pressure taping positions i and j.

2

PjPi

Pij

CCC

PiC and PjC are coefficient of pressure at i and j taping positions.

wind turbine terminologies

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