A Project on Wind Turbine Energy

8/16/2019 A Project on Wind Turbine Energy

1/13


2/13

4. Ho many turbines ill the )ry -a!e Wind +oer +ro&ect have in place hen it is

finished7

0. What is the anticipated yearly energy output in megaatts7

8. Ho many averagesi#ed homes could the )ry -a!e Wind +oer +ro&ect potentially

supply poer to7

9. What maximum height ill the turbines reach7

:. Ho many tons is the combined eight of the toer and nacelle7;. $t hat speed ill a turbine spin in order to first be able to generate electricity7


3/13

-et%s first loo! at the area sept out by the blades. $ccording to the )anish Wind Energy

$ssociation, the folloing graphic shos !iloatt output for various rotor diameter si#es.

"as! 8' $nser5do the folloing.

C. Ho long is the rotor diameter for a typical ;11 @W electrical generator7

2. "he largest rotor diameter pictured above is C1 meters. What is the area of the circle

sept out ith that rotor diameter7

41. *reate a spreadsheet of ordered pairs ith rotor diameter as your independent

variable and @W produced as your dependent variable. Draph your data and

comment on the nature of the data points. $re they linear7

44. un a (uartic regression on your data and comment about the fit of your 9 th degree

polynomial.

40. Sho mathematically that if you double your diameter, you%ll multiply your sept

out area by a factor of four.

Bo that e !no the rotor diameter ill affect the amount of energy harvested from the

ind, let%s tal! about the speed of the ind.

Wind speed usually increases ith an increase in elevation. "his phenomenon is called

“ind shear”. Why does this happen7 "hin! of the ground as causing friction, so the ind

travels sloer near the ground /rubbing against the ground slos it don3. "here are

specific “roughness” values for different types of ground surfaces. "here exist several

mathematical models to determine the speed of the ind at varying heights above the

ground. "o very common formulas for predicting ho a change in elevation ill affect the

speed of the ind are the Wind Speed -ogarithmic E(uation and the Wind Speed +oer

E(uation.

"he Wind Speed -ogarithmic E(uation'

ln

ln

desired

unknown known

known

height

Velecity Velocityheight

β

β

÷ = ÷


4/13

"he value, β , is called the roughness constant and has typical values shon in the tablebelo.

"errain )escription Surface oughness -ength, β , /m3

ery smooth, ice or mud 1.11114

*alm open sea 1.1110Flon sea 1.111:

Sno surface 1.118

-an grass 1.11C

ough pasture 1.14

Gallo ground 1.18

*rops 1.1:

Ge trees 1.4

Aany trees, hedges, fe buildings 1.0:

Gorest and oodlands 1.:

Suburbs 4.:

*enters of cities ith tall buildings 8.1

"he Wind Speed +oer E(uation'

desired unknown known

known

height Velecity Velocity

height

α

= ÷

"he exponent,α , is called the wind shear exponent . $ table of common ind shear exponentvalues follos

"errain )escription Wind Shear Exponent, α Smooth, hard ground, la!e or ocean 1.41

Short grass on untilled soil 1.49

-evel country ith foothigh grass 1.4;

"all ro crops, hedges, a fe trees 1.01

Aany trees and occasional building 1.00 I 1.09

Wooded country I small tons and suburbs 1.0C I 1.81

Jrban areas ith tall buildings 1.9

"as! 9'

$ generally recogni#ed Krule of thumbK is that ind speed increases as the 45


5/13

48. Jsing the Wind Speed +oer E(uation ith1

7α = calculate the folloing'

a. Speed at the rotor height.

b. Speed at the loest blade tip height.

c. Speed at the highest blade tip height.

49. Lnstead of using the Wind Speed +oer E(uation repeat number 4: using the Wind

Speed -ogarithmic E(uation ith 0.02β = .

4:. Ho do your results compare in parts 4 M 07

4;. Ln order to determine if a proposed site offers enough ind a “ind map” is

consulted. Examine $ri#ona%s ind map using the lin! belo. Where are the indiest

places in $ri#ona7

http'55.indpoeringamerica.gov5ind6resource6maps.asp7stateab=a#

4


6/13

b. In which direction quadrant (NE, NW, SE, SW does the least amount of wind flow from.

c. Would you characteri!e the winds at this location as coming from ageneral direction or would you consider them "ariable?

Ho Auch Energy and +oer )oes the Wind Have7

$s ind stri!es the rotor, the !inetic energy of the ind is converted into

mechanical energy as the rotor turns. We no as! this simple (uestion' “Ho much !inetic

energy and poer does the ind contain for our rotor diameter7”

Grom physics, the amount of !inetic energy a moving amount of air has is given by'

21

2kinetic E mv=

Where andm mass v velocity= = .

"he mass of floing air per unit time /mass flo rate3 that stri!es our rotor is given by

_ ( )mass air density area of rotor velocity Av ρ = × × =

Lf e substitute our mass flo rate into our !inetic energy e(uation e get the available

power of the ind'

( ) 2 31 1

2 2available

P Av v Av ρ ρ = =


7/13

"as! :'

$nser the folloing'

4C. What is the affect on the poer available if e double our rotor%s radius7 What isthe percentage increase7

42. What is the affect on the poer available if e double our ind speed7 What is the

percentage increase7

01. Lt is said “Jse as tall a ind turbine as possible.” Explain hy that ould be the

case.

04. Jsing our Wind Speed +oer E(uation, sho that our poer e(uation from above

can be ritten as

0

3

3

0

1

2

h P Av

h

α

ρ

= ÷

Where

0 0known speed for height

desired height

wind shear exponent value

v h

h

α

=

=

=

00. Suppose e currently have a ind turbine ith hub height of :1 m on a flat grassy

plain. Gurthermore e observe that at a height of 41 m the average ind speed is 41

m5s. Lf e sap out this turbine ith one that is 411 m tall at the hub height, hat

increase in poer ill the ind hold /assume same rotor diameter and air density and

1

7

α = 37

Ho Auch +oer *an a Wind "urbine Harvest Grom the Wind7

Ln 4242, $lbert Fet# concluded that no ind turbine can convert more than 4;50<

/about :2.8P3 of the !inetic energy of the ind into mechanical energy at the rotor. What

this means is that the theoretical maximum poer efficiency of any design of ind turbine is

about :2P. "his is called the Fet# -imit or Fet#% -a. Ln reality, current ind turbines are

only capable of extracting somehere beteen 8: I 9:P of the ind%s poer by the turbine.

"a!ing into account the gearbox, bearings, generator, and other elements, only about 81P

of the ind%s poer is actually converted into usable electricity. -et%s derive Fet#% -imit.

*onsider the diagram shon belo'


8/13

$s ind moves from lefttoright, Fet# proved that the mass of air passing through the rotor

S is given by

1 2

2

v vm A ρ

+ = ÷

/43

Where ρ is the air density, A is the area sept out by the rotor, and1 2

2

v v+is the ind

velocity at the rotor /note' Fet# shoed that this is &ust the average velocity of the

undisturbed ind velocities before and after the rotor3.

"he ind%s change in !inetic energy is given by'

( )2 2 2 21 2 1 21 1 1

2 2 2in out KE KE mv mv m v v− = − = − /03

"as! ;.

08. Jsing e(uations /43 and /03 from above, sho that the poer extracted by the rotor

is given by.

( )3 2 2 31 1 2 2 1 2

extracted

A P v v v v v v

ρ = − + −

"he e(uation above shos us that the poer extracted from the ind is determined by

the density of the air / ρ 3, the area sept out by the rotor / A3, and the velocity of the

moving air before and after the rotor / 1 2!v v 3.

http://en.wikipedia.org/wiki/File:Betz_tube.jpg


9/13

09. Suppose the velocity after the rotor is #ero. What implications does this have for the

turbine%s rotor and the volume of air after the turbine7 Ls any poer extracted7

0:. Suppose the velocity of the air after the turbine is the same as the velocity of air

before the turbine. What implication does this hold for our model7

0;. Sho that the ratio of the poer extracted from the ind to the poer of

undisturbed ind is given by'

( )2 3

2 2 2

1 2 2 3

1 1 1

1" 1

2

extracted

wind

P v v vC v v

P v v v

= = − + − ÷

We call ( )1 2"C v v the “poer coefficient” and Fet# established that this value is

maximal at 4;50


10/13

Ho Should Wind "urbines Fe $rranged7

Wind turbines are large mechanical devices hich dramatically slo don the natural flo

of the ind. Fecause of this, e cannot place one turbine slightly behind the other. "he

ind%s speed is reduced behind the rotor blades and turbulence /a!e3 is caused. "hus,

there must be sufficient space so that the ind can “recover” before it stri!es the next

turbine. $lthough accused of being doctored, this photo of the Horns ev OffShore Wind

Garm in )enmar! is (uite interestingR ou can observe the “a!e” behind each turbine.

"here exist very complex mathematical models for both the modeling of the ind%s a!e

after passing through a turbine and the placement of the individual turbines to optimi#e the

energy harvested for a particular locale. "here are, hoever, some elementary practical

guidelines. Gor example, a simple rule of thumb is to space the turbines ith hori#ontal M

vertical spacings of so many rotor diameters. Gor the farm pictured belo, the turbines

follo the spacing rule of 9 rotor diameters apart hori#ontally and < rotor diameters apart

vertically /in the ind%s direction3.

Denerally, the lay of the land and the direction of the prevailing ind ill determine

ho the turbines ill be placed. On ridgelines or offshore at a particular ater depth, it isnot uncommon to see a long ro of turbines.


11/13

Gor large flat areas onshore or stable depths offshore, arrayed patterns are often seen.

+apalote *ree! Wind Garm, San +atricio, "exas

#orse #ollow Wind Energy $enter % is the world&s largest wind farm at ').)megawatt (*W capacity. It consists of +- E Energy -.) *W wind turbines and-/ Siemens +. *W wind turbines spread o"er nearly 0',/// acres (-/ 1m2 of land in 3aylor and Nolan $ounty, 3e4as.

Deneral *omments about Wind Energy

http://2.bp.blogspot.com/_osrVjnPbdEM/SXmtdL3SHeI/AAAAAAAAFZs/YiIv45HTgso/s400/San_Gorgonio%2BPass_Wind_Farm_3.jpg


12/13

"here are many ind farms being built both on land and offshore throughout the orld.

Gor each site, a fe of the important (uestions to be ansered include'

• What is the topography of the site7

• Ho should the turbines be placed in order to maximi#e the harvesting potential of

the site7

5ri!ona6s 7ry 8a1e Wind 9ower 9ro:ect

• What environmental impact ill the site impart7

• What costs are associated ith this site and ill the harvesting potential lend this

site feasible from a costbenefit standpoint7

Wind energy ill continue to share a portion of $merica%s energy base. Lt on%t become the

prevailing energy source due to the large saths of land or sea needed to create substantial

farms but it does offer significant benefits over traditional fossil fuels. $ccording to the

)epartment of Energy, about 2P percent of $merica%s energy consumption is from ind

energy hile ind production composes less than 4P of our energy sources.

http://www.eia.doe.gov/energyexplained/images/charts/us_energy_consumption_by_energy_source-large.jpg


13/13

88. )espite the limited amount of ind energy used at present, the J.S. )epartment of

Energy has sought an ambitious goal for ind energy%s contribution by 0181. Jse the

folloing ebsite belo to anser this (uestion' Want percentage of $merica%s energy

demand does the )OE hope ind energy can meet7

http'554.eere.energy.gov5indandhydro5ind60181.html

"o *lose' *reative Ainds WantedR

"he push for alternative sources of energy and energy harvesting has opened thedoor for creative thin!ers. $s a student, you may ish to explore options in this groing

field. @eep in mind that traditional engineering fields are being offshored by ma&or

companies /opinions aside3 and it is the ne cutting edge technologies hich offer the most

promising &ob prospects. Bot only ill they emerge at the forefront of policy decisions but

they ill also offer the most flexibility and entrepreneurial opportunities. Who ould have

thought /except perhaps Fen&amin Gran!lin3 that something as simple as a !ite may become

a ma&or player in the future of energy production7 Fut “airborne ind turbine technology

“is not a myth. En&oy the video and company sites lin!ed belo.

Wind captured by !ites'

http'55!itegen.com5 *ool Ltalian ind !ite company /lin! for English at the right3

http'55.ma!anipoer.com5 Wind @ite company

ideo from J.@.

http'55.guardian.co.u!5environment5011C5aug5185reneableenergy.energy
http://www1.eere.energy.gov/windandhydro/wind_2030.htmlhttp://kitegen.com/http://www.makanipower.com/http://www.makanipower.com/http://www.guardian.co.uk/environment/2008/aug/03/renewableenergy.energyhttp://www.eia.doe.gov/energyexplained/images/charts/us_energy_production_by_energy_source-large.gif%20http://www1.eere.energy.gov/windandhydro/wind_2030.htmlhttp://kitegen.com/http://www.makanipower.com/http://www.guardian.co.uk/environment/2008/aug/03/renewableenergy.energy

A Project on Wind Turbine Energy

Documents

Transcript of A Project on Wind Turbine Energy