FWE Assignment Solution 1

8/12/2019 FWE Assignment Solution 1

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PANDIT DEENDAYAL PETROLEUM UNIVERSITY

SCHOOL OF TECHNOLOGY

Fundamental of Wind Energy (ME708) Assignment Solution

1 A Discuss : Cost of wind energy

Ans !"e cost of #ind energy is com$ara%le to &on'entionalfuel%ased energy* #"en cost of

green"ouse gas emissions is ta+en into account A'erage cost of energy from coal is a%out,80 $er MW"* #"ile #ind energy at a site #it" a'erage annual #ind s$eed of 7 m-s isslig"tly less t"an ,80 $er MW" Figure %elo# is a $lot of le'eli.ed cost of energy from coal*natural gas* nuclear* and ons"ore and offs"ore #ind for a'erage #ind s$eed in t"e range of/ to 10 m-s!"e ad'antage of #ind is t"at it "as no fuel cost According to t"e DE re$ort* t"e amountof economically 'ia%le ons"ore #ind $o#er is 8000 W t"at can %e $roduced at a cost of283 $er MW" or less

Fig. Levelized cost of energy from different sources. Costs are in euros per MWh. Cost ofwind energy is a function of wind speed

1 4 Discuss : Benefits of wind energy

Ans 4enefits of #ind energy are listed %elo#

5rimary %enefits is en'ironmental %enefits

Secondary %enefits is cost com$are to &on'entional source of $o#er li+e coal*natural gas* nuclear

Wind energy $roduction results in .ero emissions

Wind energy is among t"e c"ea$est sources of rene#a%le energy #ind energy isa'aila%le in a%undance in most &ountries

W"ere e'er electricity grid is not $ossi%le t"ere #e can use as $rime source ofelectricity

6 A E$lain : Kinetic energy of wind

Ans The kinetic energy contained in wind is:

E = m'6 Cylinder of air in front of therotor.


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Fundamental of Wind Energy (ME708) Assignment Solution!"e mass (m) from #"ic" energy is etracted is t"emass contained in t"e 'olume of air t"at #ill flo#t"roug" t"e rotor For a "ori.ontal ais #indtur%ine (9AW!)* t"e 'olume of air is cylindrical*as s"o#n in Fig

+inetic energy of a solid o%ect of fied mass Wit"air flo#* it is con'enient to t"in+ of mass in acylinder of air of radius r Since v m-s is t"e #inds$eed* t"e mass contained in cylinder of lengt" vmeters and radius r is t"e amount of mass t"at #ill$ass t"roug" t"e rotor of tur%ine $er second ;t is* t"erefore* con'enient to use mass $ersecond (m< )

E= m.v2

m =Av

#"ere is air density andA is t"e crosssection area m< is t"e amountof matter contained in a cylinder of air of lengt" v 5-5 = 6>r-r!"is means t"at if t"e radius is increased-decreased %y 1?* $o#er #ill increase-decrease %y6? For larger c"anges in radius* t"e a%o'e formula does not a$$ly@ for instance* a 10?increase in radius #ill lead to increase %y 61? in $o#er A 60? increase in radius #ill leadto ? increase in $o#er;f s$eed is c"anged %y a small amount and all else is constant* t"en>5-5 = B>'-'!"is means t"at if t"e s$eed is increased-decreased %y 1?* energy #ill increase-decrease %yB? 9o#e'er* if t"e #ind s$eed is increased %y 60?* t"e $o#er #ill increase %y:1-6 = v"1v

"6= (1.6)

B= 1.768!"is is a 768? increase in $o#er !"e relations"i$ %et#een $o#er and #ind s$eed* and$o#er and rotor diameter are seen in Figs %elo# :

Cubic relationship between power and wind speed for a horizontal

axis wind rotor with radius = 1 m.


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Cu#ic relationship #etween power and wind speed for a horizontal a$is wind rotor withradius % & m.

'uadratic relationship #etween power and rotor size. Wind speed is ( m!s.

& E$lain : &onser'ation of Mass

Ans For calculation of conser'ation of energy follo#ing Assum$tions are made:

All air t"at enters atA0 lea'es fromA6 Fluid flo# is streamlined and so t"ere is noloss of mass from t"e surface of t"e control 'olume

Fluid is incom$ressi%le* t"at is* t"ere is no c"ange in density


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;llustration of a control 'olume t"at follo#s streamlines t"at $ass t"roug" t"e rotor v0) vr )v6 are u$stream* rotor* and do#nstream #ind s$eedsA0) Ar ) A6 are u$stream* rotor* anddo#nstream crosssectional areas

Cnder t"ese assum$tions* conser'ation of mass is:m< =A0v0=Arvr=A6v6

#"ere v6is t"e a'erage #ind s$eed* #"ere t"e a'erage is ta+en o'er crosssectional A6@ vrisassumed to %e uniform o'erAr* #"ereAris t"e area of t"e rotor Since t"e rotor of tur%ine isetracting energy from air* t"e +inetic energy of air #ill reduce* so* v0* vr* v6

D E$lain : Conservation of energy

Ans A sim$lified conser'ation of energy euation is used initially* under t"e assum$tions listed%elo#

!otal energy = inetic energy 5ressure energy 5otential energy!"e +inetic energy is %ecause of t"e directed motion of t"e fluid@ $ressure energy is %ecauseof t"e random motion of $articles in t"e fluid@ $otential energy is %ecause of relati'e $ositionof t"e fluidAssum$tions:

Fluid is incom$ressi%le* meaning t"e density does not c"ange Gote t"at $ressure canc"ange

Fluid flo# is in'iscid* meaning t"e euation a$$lies to fluid flo# outside a %oundarylayer !"e %oundary layer is #"ere t"e friction %et#een a surface and fluid causesslo#er fluid flo#

All t"e flo# is along streamlines

!"ere is no #or+ done %y s"ear forces

!"ere is no "eat ec"ange

!"ere is no mass transfer

Helati'e $osition of fluid #it" res$ect to t"e eart"Is surface does not c"ange* t"at is*t"e $otential energy remains constant

!"e first t#o assum$tions define an ideal fluid !"e a%o'e assum$tions lead to 4ernoulliseuation:!otal energy $er unit 'olume =v6-6p = constantv+!+ is t"e +inetic energy term* #"ic" is also called t"e dynamic $ressure* andp is t"e static$ressure 4ernoullis euation* t"erefore* states t"at along a stream line #"en s$eedincreases* t"en $ressure decreases and #"en s$eed decreases* t"en $ressure increases !"e


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Fundamental of Wind Energy (ME708) Assignment Solutionmagnitude of c"ange in $ressure is go'erned %y t"e uadratic relations"i$

E E$lain : Conservation of momentum

Ans

Since t"e #ind rotor is a mac"ine t"at #or+s %y etracting +inetic energy from #ind* t"e#ind s$eed is reduced Since momentum is mass multi$lied %y s$eed* t"ere is a c"ange inmomentum According to Ge#tonIs second la#* t"e rate of c"ange of momentum in a

control 'olume is eual to t"e sum of all t"e forces acting ;n order to sim$lify t"e euations*t"e follo#ing assum$tions are reuired:

!"ere are no s"ear forces in t"e$direction!"e $ressure forces on edgesA0andA6are eual!"ere is no momentum loss or gain ot"er t"an fromA0andA6!"e euation for Ge#tonIs second la# along t"e$ais %ecomes:m


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Fundamental of Wind Energy (ME708) Assignment Solution#"ere '6 is t"e a'erage #ind s$eed at A6 A$$lying Ge#tonIs second la#Go# force eerted on rotor %y #ind:F = m


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!rite a note on wind speed measuring instrumentation li#e cap anemometer" propelleranemometer" sonic anemometer " S$%&'" ()%&'

Ans !ind Speed *easuring )nstruments are discuss as below

Cup Anemomete! "

!"e cu$ anemometer is $ro%a%ly t"e most common instrument for measuring t"e #inds$eed &u$ anemometers use t"eir rotation* #"ic" 'aries in $ro$ortion to t"e #ind s$eed* togenerate a signal !odayIs most common designs feature t"ree cu$s mounted on a smalls"aft !"e rate of rotation of t"e cu$s can %e measured %y:

mec"anical counters registering t"e num%er of rotations@

electrical or electronic 'oltage c"anges (A& or D&)@

a $"otoelectric s#itc"

!"e mec"anicalty$e anemometers indicate t"e #ind flo# in distance !"e mean #ind s$eedis o%tained %y di'iding t"e #ind flo# %y time (t"is ty$e is also called a #indrunanemometer) For remote sites* t"is ty$e of anemometer "as t"e ad'antage of not reuiring a$o#er source

Some of the earliest types of mechanical anemometers also drove a pen recorder directly.+owever" these systems were expensive and difficult to maintain.&n electronic cup anemometer gives a measurement of instantaneous wind speed. ,helower end of the rotating spindle is connected to a miniature &C or %C generator and theanalog output is converted to wind speed via a variety of methods.

,he photoelectric switch type has a disc containing up to 1- slots and a photocell. ,he

periodic passage of the slots produces pulses during each revolution of the cup.,he response and accuracy of a cup anemometer are determined by its weight" physicaldimensions" and internal friction. By changing any of these parameters" the response of theinstrument will vary. )f turbulence measurements are desired" small" lightweight" low/frictionsensors should be used. ,ypically" the most responsive cups have a distance constant ofabout 1 m. !here turbulence data are not re0uired" the cups can be larger and heavier"

with distance constants from - to m. ,his limits the maximum usable data sampling rate tono greater than once every few seconds. ,ypical accuracy values 2based on wind tunneltests3 for cup anemometers are about 4/-5.6nvironmental factors can affect cup anemometers and reduce their reliability. ,heseinclude ice or blowing dust. %ust can lodge in the bearings" causing an increase in frictionand wear and reducing anemometer wind speed readings. )f an anemometer ices up" its

rotation will slow" or completely stop" causing erroneous wind speed signals" until thesensor thaws completely. +eated cup anemometers can be used" but they re0uire asignificant source of power. Because of these problems" the assurance of reliability for cupanemometers depends on calibration and service visits. ,he fre0uency of these visitsdepends on the site environment and the value of the data.


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Cup anemometer

Pope##e Anemomete!

5ro$eller anemometers use t"e #ind %lo#ing into a $ro$eller to turn a s"aft t"at dri'es anA& or D& (most common) generator* or a lig"t c"o$$er to $roduce a $ulse signal !"edesigns used for #ind energy a$$lications "a'e a fast res$onse and %e"a'e linearly inc"anging #ind s$eeds ;n a ty$ical "ori.ontal configuration* t"e $ro$eller is +e$t facing t"e#ind %y a tail'ane* #"ic" also can %e used as a direction indicator !"e accuracy of t"isdesign is a%out 6?* similar to t"e cu$ anemometer !"e $ro$eller is usually made of$olystyrene foam or $oly$ro$yleneW"en mounted on a fied 'ertical arm* t"e $ro$eller anemometer may %e used formeasuring t"e 'ertical #ind com$onent A configuration for measuring t"ree com$onents of#ind 'elocity is s"o#n in 4elo# Figure !"e $ro$eller anemometer res$onds $rimarily to#ind $arallel to its ais* and t"e #ind $er$endicular to t"e ais "as no effect


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Son$% Anemomete!

Cltrasonic Anemometers use ultrasonic sound #a'es to measure #ind s$eed and directionWind 'elocity is measured %ased on t"e time of flig"t of sonic $ulses %et#een $airs oftransducers A re'ie# of t"eir t"eory of o$eration is gi'en %y &uer'a and San.Andres(6000)ne* t#o* or t"reedimensional flo# can %e measured 'ia signals from $airs of transducers!y$ical #ind engineering a$$lications use t#o or t"reedimensional sonic anemometers

!"e s$atial resolution is determined %y t"e $at" lengt" %et#een transducers (ty$ically 10 to60 cm) Sonic anemometers can %e used for tur%ulence measurements #it" fine tem$oralresolution (60 9. or %etter)

A%ou!t$% Dopp#e Sen!o! &SODAR'

SDAH (standing for Sound Detection And Hanging) is classified as a remote sensingsystem* since it can ma+e measurements #it"out $lacing an acti'e sensor at t"e $oint ofmeasurement Since suc" de'ices do not need tall (and e$ensi'e) to#ers for t"eir use* t"e$otential ad'antages of t"eir use are o%'ious Hemote sensing is used etensi'ely formeteorological and aeros$ace $ur$oses* %ut only in recent times "as it %een used for #ind

siting and $erformance measurementsSDAH is %ased on t"e $rinci$le of acoustic %ac+scattering ;n order to measure t"e #ind$rofile #it" SDAH* acoustic $ulses are sent 'ertically and at a small angle to t"e 'erticalFor measurement of t"reedimensional #ind 'elocity* at least t"ree %eams in differentdirections are needed !"e acoustic $ulse transmitted into t"e air e$eriences %ac+scatteringfrom $articles or fluctuations in t"e refracti'e inde of air !"ese fluctuations can %e caused%y #ind s"ear as #ell as %y tem$erature and "umidity gradients !"e acoustic energyscattered %ac+ to t"e ground is t"en collected %y micro$"ones Assuming t"at t"e sender andt"e recei'er are not se$arated* t"e SDAH configuration is referred to as a monostaticSDAH At t"e $resent time all commercial SDAHs used for #ind energy a$$lications aremonostatic (sim$lifying t"e system design and reducing its si.e)


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Fundamental of Wind Energy (ME708) Assignment Solution;f t"e local s$eed of sound is +no#n* t"e tra'el time %et#een emission and rece$tiondetermines t"e "eig"t t"e signal re$resents A c"ange in t"e acoustic freuency of t"e ec"o(Do$$ler s"ift) occurs if t"e scattering medium "as a com$onent of motion $arallel to t"e%eam motion !"us* estimation of t"e s$eed of t"e #ind s$eed $arallel to t"e %eam as afunction of "eig"t can %e carried out 'ia freuency s$ectrum analysis of t"e recei'ed %ac+

scattered signalSDAHs "a'e %een used for %ot" ons"ore and offs"ore #ind siting studies #it"measurement of #ind s$eed u$ to B00m a%o'e t"e de'icealt"oug" SDAH systems can %e commercially $urc"ased* t"e follo#ing issues "a'e arisen:

L(!e Dopp#e Sen!o! &LIDAR'

O;DAH (Oig"t Detection And Hanging)* similar to SDAH* is also classified as a remotesensing de'ice* and can similarly %e used to ma+e measurements of a t"reedimensional#ind field ;n t"is de'ice* a %eam of lig"t is emitted* t"e %eam interacts #it" t"e air and

some of t"e lig"t is scattered %ac+ to t"e O;DAH !"e returned lig"t is analy.ed to determinet"e s$eed and distances to t"e $articles from #"ic" it #as scattered ;n addition* t"e %asicO;DAH $rinci$le relies on t"e measurement of t"e Do$$ler s"ift of radiation scattered %ynatural aerosols t"at are carried %y t"e #indO;DAHs "a'e %een used etensi'ely in meteorological and aeros$ace a$$lications* #it" t"ecost of meteorological O;DAH systems %eing uite "ig" 9o#e'er* de'elo$ments incommercially a'aila%le O;DAH systems "a'e $roduced lo#er cost systems for #ind s$eeddetermination at "eig"ts of interest in #ind energy a$$lications ;n addition* eye safetyconcerns "a'e %een o'ercome since t"e maority of O;DAH lasers emit at t"e eyesafe#a'elengt" of 13 microns Csing t"ese ne# systems* O;DAH "as most recently %eena$$lied to %ot" ons"ore and offs"ore #ind system a$$lications

At t"e $resent time* t"ere are t#o ty$es of commercial O;DAH de'ice a'aila%le for #indengineering a$$lications: (1) a constant #a'e* 'aria%le focus design* and (6) a $ulsedO;DAH #it" a fied focus Wind s$eeds at "eig"ts u$ to 600m "a'e %een measured %y %ot"ty$es of O;DAH systemAs an eam$le of an a$$lication of a constant #a'e O;DAH system* a $orta%le and com$actO;DAH system #as used to determine "ori.ontal and 'ertical #ind s$eed and direction at"eig"ts u$ to 600 mAs s"o#n in Figure %elo#* t"e O;DAH %eam is offset at B0 degrees tot"e 'ertical !"e %eam scans as it re'ol'es at one re'olution $er second As t"e %eam rotatesit interce$ts t"e #ind at different angles* t"ere%y %uilding u$ a #ind s$eed ma$ around a discof air ;n a ty$ical o$eration* t"ree scans are $erformed at eac" "eig"t* and #indmeasurements are ta+en at fi'e "eig"ts


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-chematic of conically scanned L/A0 system

3 9o# #ind data analysis $erformed

Ans !"e data $roduced %y a #ind monitoring system can %e analy.ed in a num%er of #ays!"ese may include* %ut are not limited to:

a'erage "ori.ontal #ind s$eeds o'er s$ecified time inter'als@

'ariations in t"e "ori.ontal #ind s$eed o'er t"e sam$ling inter'als (standard de'iation*

tur%ulence intensity* maima)@

a'erage "ori.ontal #ind direction@

'ariations in t"e "ori.ontal #ind direction o'er t"e sam$ling inter'als (standard

de'iation)@

s$eed and direction distri%utions@

$ersistence@

determining gust $arameters@

statistical analysis* including autocorrelation* $o#er s$ectral density* lengt" and time

scales* and s$atial and time correlations #it" near%y measurements@

steady and fluctuating u* '* # #ind com$onents@

diurnal* seasonal* annual* interannual and directional 'ariations of any of t"e a%o'e

$arametersSome mention "as %een made of eac" of t"ese measures of #ind data* ece$t for $ersistence5ersistence is t"e duration of t"e #ind s$eed #it"in a gi'en #ind s$eed range Also*"istograms of t"e freuency of continuous $eriods of #ind %et#een t"e cutin and cutout

#ind s$eeds #ould $ro'ide information on t"e e$ected lengt" of $eriods of continuoustur%ine o$erationA#ind rose is a diagram s"o#ing t"e tem$oral distri%ution of #ind direction and a.imut"aldistri%ution of #ind s$eed at a gi'en location A #ind rose (an eam$le of #"ic" is s"o#n inFigure %elo#) is a con'enient tool for dis$laying anemometer data (#ind s$eed anddirection) for siting analysis !"is figure illustrates t"e most common form* #"ic" consistsof eually s$aced concentric circles #it" 1/ eually s$aced radial lines (eac" re$resents acom$ass $oint) !"e line lengt" is $ro$ortional to t"e freuency of t"e #ind from t"ecom$ass $oint* #it" t"e circles forming a scale !"e freuency of calm conditions isindicated in t"e center !"e longest lines identify t"e $re'ailing #ind directions Wind rosesgenerally are used to re$resent annual* seasonal* or mont"ly data


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E$ample of a wind rose diagram

/ A Define and deri'e e$ression for Po)e *en!$t+

Ans 5o#er density gi'es t"e measure of $o#er a'aila%le in unit area

5o#er density is defined as:

;f t"e statistical distri%ution of #ind is ignored and it is assumed t"at t"ere is no 'ariation in

#ind s$eed* t"en t"e $o#er density is incorrectly com$uted

#"ere ' is t"e a'erage #ind s$eed 9o#e'er* if t"e energy density is com$uted correctly#"ile ta+ing into account $ro%a%ility density of #ind s$eed* t"en t"e $o#er density num%ersare 'ery different

#"ere $d(') is t"eWei%ull $ro%a%ility density function


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llustration of the power density function for wind speed with a Wei#ull distri#ution A % (

and 1 % +. 2he mean wind speed is 3.45 m!s. 6otice the power density curve pea1s at && m!s.

4 Define and deri'e e$ression for ,$n* %#(!!e!

Ans As a con'ention* t"e strengt" of #ind at a site is classified %ased on $o#er density at anele'ation of 30 m a%o'e t"e ground le'el (AO) !a%le %elo# lists t"e definition of #indclasses in terms of $o#er density at 10 and 30 mB For sa+e of con'enience* #ind s$eedranges are associated #it" t"e $o#er density ranges Gote* t"is ma$$ing of $o#er density to#ind s$eed is correct only if 1 = 6* t"at is* it is only correct if #ind at t"e location "as aHayleig" distri%utionAlt"oug" #ind class definition in terms of #ind s$eed range is #idely used* it is ana$$roimationA $o$ular misconce$tion is t"at #ind class can %e determined if t"e annual

a'erage #ind s$eed at 30 m is gi'en Alt"oug" t"is #or+s for certain $ro%a%ility densityfunctions of #ind s$eed* it may not al#ays yield t"e correct #ind class

/efinition of Wind Classes

& Define and deri'e e$ression for ,$n* !-e(

Ans Wind s"ear descri%es t"e c"ange in #ind s$eed as a function of "eig"t Assuming t"ere is nosli$$age on t"e surface* t"e surface #ind s$eed is .ero !"at is* #ind s$eed is .ero at an

ele'ation of .ero !"ere are t#o met"ods to descri%e s"ear: 5o#er la#$rofile and logarit"m


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Fundamental of Wind Energy (ME708) Assignment Solution$rofile!"e $o#er la# is t"e most common met"od to descri%e t"e relations"i$ of #ind s$eed and"eig"t !"is is an engineering a$$roimation and must %e used #it" caution

#"ere '6and '1are #ind s$eeds at "eig"ts "6 and "1* and e$onent P is called #ind s"earAn alternate met"od to etra$olate #ind s$eed is to use t"e logarit"mic $rofile* #"ic" usesroug"ness of t"e surface

#"ere70 is called t"e roug"ness lengt" ;f #ind s$eed 81 is a'aila%le at h1= 10 m* t"ena%o'e E may %e used to com$ute 86.!"e 'alue of s"ear can t"en %e deri'ed using a%o'e t#o Es as:

lot of the ratio of wind speed to ratio of height for different values of shear.

S"ear* t"erefore* de$ends on t"e "eig"ts and roug"ness lengt"

7 Deri'e t"e e$ression for t"e maimum $o#er coefficient for t"e rotor dis+ #it" res$ect to#ind tur%ine using 4et. t"eory

Ans 4et. $ostulated a t"eory a%out t"e efficiency of rotor%ased tur%ines Csing sim$le conce$tsof conser'ation of mass* momentum* and energy* "e $ostulated t"at a #ind tur%ine #it" adiscli+e rotor cannot ca$ture more t"an 3JB? of energy contained in a mass of air t"at #ill$ass t"roug" t"e rotor !"e 4et. limit is deri'ed netA$$lying conser'ation of mass* in control 'olumeA0*Ar* andA6#it" constant densityA0'0= Ar'r= A6'6


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Fundamental of Wind Energy (ME708) Assignment Solution#"ere '6 is t"e a'erage #ind s$eed at A6 A$$lying Ge#tonIs second la#Go# force eerted on rotor %y #ind:F = m


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Fundamental of Wind Energy (ME708) Assignment SolutionAns !"e lift force $er unit lengt" of %lade is:

Oift force is traditionally e$ressed in terms of a lift coefficient (CL ) as:

#"ere - is t"e area of t"e %lade* #"ic" is eual to c"ord lengt" (c) multi$lied %y t"e lengt"of t"e %lade (l)

!"is is a t"eoretical relations"i$ %et#een CLand 9* t"e attac+ angle Em$irically* for small'alues of 9* t"e relations"i$ is linear 9o# small de$ends on t"e airfoil design@ ty$ical'alues for al$"a are in t"e range of K13 to 13R utside t"is range* t"e linear relations"i$%et#een CL and Q ceases to eist As Q increase* t"e lift dro$s off resulting in a stallconditionSalient features of t"e coefficient of lift cur'e in Figure are %elo# are:

&ur'es are o%tained em$irically %y conducting e$eriments on s$ecific airfoil s"a$es

;n t"e linear region* t"e slo$e is 6:

For nonsymmetrical airfoils #it" cam%er line (line t"at is euidistant from u$$er andlo#er surface of t"e airfoil) t"at is "ig"er t"an c"ord line* t"e entire lift cur'e s"ifts u$*resulting in $ositi'e lift for .ero angle of attac+

;eneral CLform of the coefficient of lift as a function of attac1 angle for a symmetric airfoil.

J 5lot coefficient of drag 's angle of attac+

Ans A uestion 9o# can $ressure drag %e reducedT !"e ans#er is* %y mo'ing t"e %oundary

layer se$aration $oint closer to t"e trailing edge !"e t#o $rimary factors t"at influence t"elocation of %oundary layer se$aration $oint are angle of attac+ and surface roug"ness As t"eangle of attac+ increases* t"e se$aration $oint mo'es closer to t"e leading edge !"e $ressuredrag is $ro$ortional to t"e suare of t"e attac+ angle!"e drag force is traditionally e$ressed in terms of a drag coefficient (C/) as:

#"ere &fD* &$Dare coefficients of s+infriction drag and $ressure drag For normal #ind

s$eeds (UU s$eed of sound)* s+infriction drag is small and t"e $ressure drag is larger Since


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Fundamental of Wind Energy (ME708) Assignment Solution&Ois a linear function of Q* and &$Dis a uadratic function of Q* As s"o#n in %elo# Fig !"erelations"i$ %et#een drag and lift at normal #ind s$eeds and small 'alues of Q (less t"an 13

/rag as a function of attac1 angle.

degrees) is:

W"ere is t"e s$an#ise efficiency factor*Ar is t"e as$ect ratio

10

Discuss flo# of fluid o'er an aerofoil and e$lain different regions for a flo# o'er anaerofoil

Ans

Airfoils are structures #it" s$ecific geometric s"a$es t"at are used to generate mec"anicalforces due to t"e relati'e motion of t"e airfoil and a surrounding fluid Wind tur%ine %ladesuse airfoils to de'elo$ mec"anical $o#er !"e crosssections of #ind tur%ine %lades "a'e t"es"a$e of airfoils!"e mean cam%er line is t"e locus of $oints "alf#ay %et#een t"e u$$er and lo#er surfacesof t"e airfoil!"e straig"t line connecting t"e leading and trailing edges is t"e c"ord line of t"e airfoil* andt"e distance from t"e leading to t"e trailing edge measured along t"e c"ord line is designatedt"e c"ord* c* of t"e airfoilFinally* t"e angle of attac+* a* is defined as t"e angle %et#een t"e relati'e #ind (Crel) and

t"e c"ord line


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Fundamental of Wind Energy (ME708) Assignment SolutionAir flo# o'er an airfoil $roduces a distri%ution of forces o'er t"e airfoil surface !"e flo#'elocity o'er airfoils increases o'er t"e con'e surface resulting in lo#er a'erage $ressureon t"e VsuctionI side of t"e airfoil com$ared #it" t"e conca'e or V$ressureI side of t"eairfoil Mean#"ile* 'iscous friction %et#een t"e air and t"e airfoil surface slo#s t"e air flo#to some etent net to t"e surface

L$.t .o%e defined to %e $er$endicular to direction of t"e oncoming air flo# !"e lift forceis a conseuence of t"e uneual $ressure on t"e u$$er and lo#er airfoil surfacesD( .o%e defined to %e $arallel to t"e direction of t"e oncoming air flo# !"e drag forceis due %ot" to 'iscous friction forces at t"e surface of t"e airfoil and to uneual $ressure ont"e airfoil surfaces facing to#ard and a#ay from t"e oncoming flo#P$t%-$n moment defined to %e a%out an ais $er$endicular to t"e airfoil crosssection!"e lift* drag* and $itc"ing moment coefficients of an airfoil are generated %y t"e $ressure'ariation o'er t"e airfoil surface and t"e friction %et#een t"e air and t"e airfoil!"e $ressure 'ariations are caused %y c"anges in air 'elocity t"at can %e understood using4ernoulliIs $rinci$le* #"ic" states t"at t"e sum of t"e static $ressure and t"e dynamic$ressure (assuming frictionless flo#) are constant:

W"ere $ is t"e static $ressure and C is t"e local 'elocity along t"e airfoil surface As t"e airflo# accelerates around t"e rounded leading edge* t"e $ressure dro$s* resulting in a negati'e$ressure gradient As t"e air flo# a$$roac"es t"e trailing edge* it decelerates and t"e surface$ressure increases* resulting in a $ositi'e $ressure gradient ;f* gi'en t"e airfoil designand t"e angle of attac+* t"e air s$eeds u$ more o'er t"e u$$er surface t"an o'er t"e lo#ersurface of t"e airfoil* t"en t"ere is a net lift force Similarly* t"e $itc"ing moment is afunction of t"e integral of t"e moments of t"e $ressure forces a%out t"e uarter c"ord o'ert"e surface of t"e airfoil

11

W"at is t"e difference %et#een constant s$eed tur%ine and 'aria%le s$eed tur%ineT E$lain#it" necessary c"arts

Ans ;n &onstant S$eed !ur%ine (&S!) generator is directly connected to grid #"ere as inaria%le S$eed !ur%ine (S!) generator is not directly connected to grid;n &S! A gridconnected async"ronous generator is t"e sim$lest and c"ea$est ty$e ofgenerator %ecause t"e out$ut energy is at t"e grid freuency W"ere as in S! t"ere is also areuirement of $o#er electronics to rectify or in'ert (A&7D&* D&7A&) So generator iscostly;n &S! constantrotor s$eed tur%ines are una%le to deli'er t"e o$timal $o#er out$ut atdifferent #ind s$eed #"ere as S! are ena%le to deli'er t"e o$timal $o#er out$ut at


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Fundamental of Wind Energy (ME708) Assignment Solution'aria%le #ind s$eed

ower output versus rotor speed for different wind speeds. ower curves for fi$ed speed

rotor and varia#le speed rotor are illustrated. $ 4?.

16 D$!%u!! ene(#$!e* oto *e!$n po%e*ue .o !pe%$.$%%on*$t$on!0

Ans

1B

A 9o# #ill you design a #ind measurement cam$aign %ased onA Gum%er of met to#ers4 5lacement of met to#ers

Ans Wind measurement cam$aign "as $rimary o%ecti'e is to im$ro'e accuracy of $rediction ofenergy out$ut of t"e #ind $roect* ot"er factors li+e economics and $roect sc"eduleSo main factors are as %elo#

Gum%er of met to#ers

5lacement of met to#ers

a #ind measurement cam$aign must start #it" #"at is +no#n and design a $rocess t"at caneconomically generate reasona%ly accurate energy $redictions A $rocess for designing a#ind measurement cam$aign is descri%ed %elo# ;t may %e ada$ted to meet a $roectss$ecific need1 &onduct a $reliminary #ind resource assessment of t"e area under consideration !"isa$$lies to %ot" single tur%ine and #indfarm installations !"e outcome of t"e $reliminary#ind assessment #ill %e a #ind resource ma$ of suita%le granularity For t"e $ur$oses oft"is discussion* it is assumed t"at #ind resources are a'aila%le for a 600m 600mgrid !"eresource ma$ may %e %ased on com$uter simulations using numerical #eat"er $redictionmodels or #ind resource$rediction model li+e WAs5 or ot"ers !"e source of t"e #ind data

for t"ese models may %e 10m air$ort data and-or reanalysis data from Gational &enter for


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Fundamental of Wind Energy (ME708) Assignment SolutionAtmos$"eric Hesearc" (G&AH)6 !"e $reliminary location of Wind !ur%ine enerators (W!s) may %e com$uted %yrunning a layout o$timi.ation model (eam$le $timi.e in Wind5H) #it" #ind resourcema$ from ste$ (1) and a 'ariety of constraints &onstraints include maimum #indfarmca$acity* minimum ca$acity factor* tur%ine to#er "eig"t and rotor diameter* distances

%et#een tur%ines* and ot"er set%ac+ criteria li+e distance %et#een tur%ine and $ro$erty%oundary* $u%lic roads* transmission* and in"a%ited areas ;n t"is $"ase* t"e constraints areguidelines rat"er t"an $recise For a single tur%ine case* a location #it" t"e "ig"est #indresource t"at satisfies all t"e constraints is t"e location of t"e metto#er For a #ind farm* goto ste$ (B)B ;n t"e $reliminary W! layout* form clusters of W!s ;f t"e #ind farm is in a com$leterrain* t"en 3 to 7 W!s may %e grou$ed into one cluster ;f it is a sim$ler terrain #it" 'erylittle c"anges in ele'ation and roug"ness* t"en 10 to 16 W!s may %e grou$ed into onecluster !"e clusters #ill %e %ased on distance &lusters are %est formed 'isually@ t"e %ordersof clusters may %e dra#n manually on a &om$uter Aided Design (&AD) dra#ing or on$a$er !"e ratio %et#een W! and metto#ers of 3 to 7* or 10 to 16 are normal guidelines

for determining num%er of fied metto#ers for #ind measurement Harely #ill all clusters"a'e t"e same num%er of W! ;n eac" cluster* find t"e median #ind s$eed W! !"is W! location or a location in t"e'icinity #ould %e a location for $lacement of metto#er Measuring at t"e %est or #orst#ind resource location in t"e cluster #ould yield #ind measurements t"at "a'e to %e eit"eretra$olated do#n or etra$olated u$ to all $oints in t"e cluster* #"ic" #ould lead to "ig"erinaccuracies Gormally* a set of t#o or t"ree locations is c"osen in eac" cluster For instance*t"e t"ree locations are: Oocation #it" median #ind s$eed and t"e t#o locations #it" t"esmallest difference #it" t"e median #ind s$eed3 !"e goal of t"is ste$ is to $ic+ one location in eac" cluster suc" t"at* for t"e #ind farm as a#"ole* t"e metto#er locations are sufficiently s$read out geogra$"ically !"is ste$ is %estdone 'isually* starting #it" t"e median #ind s$eed location in eac" cluster and t"eneamining t"e $roimity of t"ese locations ;f t"e median locations of t#o clusters aregeogra$"ically close* t"en alternate locations are c"osen from t"e set

FWE Assignment Solution 1

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