Effective Performance Improvement of Hawt Blades using Optimization Technique Process

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1 Intentionl Jounl of Engineeing nd Mngement Resech, Vol.-, Issue-1, Febuy 01 ISSN No.: Pges: -9 Effective Pefomnce Impovement of Hwt Bldes using Optimiztion Technique Pocess R. SenthilKum 1, R.Mnimn, R. Rmdoss,V.Goplkishnn 4 1, Resech Schol, Mechnicl Engineeing, Annmli Univesity, INIA. Resech Schol, Mechnicl Engineeing, Pondichey Engineeing College, INIA. Assistnt Pofesso, Mechnicl Engineeing, EGS Pilli Engineeing College, Ngpttinm, INIA. ABSTRACT This ppe pesents n optiml solution fo the detemintion of eodynmic pefomnce chcteistics of hoizontl xis wind tubines. Bsed on the diffeent nlyticl methods exmined in the clcultion of xil nd tngentil induction fctos ( & ), the vition in Co-efficient of pefomnce (Cp) possibly is noted. The ppe includes the cse study which involves the pediction though BEM (Blde Element Momentum method) nd compison of vious design pmetes including Angle of Attck (AOA), Twist ngle (θ), influencing the ovell pefomnce. Results fo typicl ifoil s-section show tht the optimum ngle of ttck nd optimum twist ngle of the blde impoves the pefomnce of the wind tubine. A coding technique hs been suggested which demonsttes the wok done in the evlution of optimum pefomnce of HAWT on the bsis of litetue. Keywods: Angle of ttck, Axil nd Tngentil induction fctos, BEM. I. INTROUCTION In the moden e of science & Technology, thee hs been vst impovement in the need fo enegy esouces. Since fo vey long decde the mjo esouce ws col, but lte fte the poblems with envionment begn, the need fo ltentive clen nd eco-fiendly souces wee much sensed. The Sun is the pimy souce of ll enegy s. Wind enegy is nothing but the sol enegy tnsfomed to kinetic enegy Theefoe, in the field of wind enegy, the incesing demnd of efficient wind tubines hs led to the development of numeous eodynmic nlysis models. Wind tubines with n optimized mximum pefomnce my become evolution in the field of enewble enegy s the instllment t of tubines is much lesse when comped to most of the clen enegy souces. Vious eseches e being done fo the optimiztion of wind tubines using diffeent techniques. The most commonly suggested method fo nlyzing the ifoils is Blde Element Momentum theoy (BEM)[1,]. The BEM theoy is bsed on the Gluet popelle theoy [], modified fo ppliction to wind tubines [,5]. Gluet [6,7] oiginted the bsic eodynmic nlysis concepts of iscew popelles nd windmills. Wilson et l. [8,9] extended Gluet s wok nd pesented step by step pocedue fo clculting pefomnce chcteistics of wind tubines. Theefoe, by pplying the momentum nd ngul momentum consevtion equtions, we cn exmine the foces geneted by the eofoil lift nd dg coefficients t vious sections long the blde which cn be solved by itetion pocess [10]. Accoding to [11] design pmete choice is citicl fo optimizing wind tubine pefomnce. Fo ny fixed dimete thee e vious pmetes influencing enegy poduction: oto ottion velocity, blde numbe, ifoil chod distibution nd longitudinl blde twist. In this ppe detiled litetue study is done on the xil nd induction fctos using the BEM method which includes cse study of m long blde design. Thee is bief study done on the selection of pofiles mong NACA on the bsis of vious selection citei. In this ppe, n extensive study is mde to nlyze the effective pefomnce of the bove sid ifoils. Afte optimizing the pofile, bsed on highest lift nd dg, n itetion pocess is included which showed compison of the obtined Cp (Betz poved mximum possible Cp is 59.%) fo vious Angle of Attck nd velocities on the optimized pofile. The wok hs been concluded with the suggestion of flowcht fo the design pocedue fo the itetion pocess. II. BAE EEMENT MOMENTUM THEORY The mthemticl model fo the fluid dynmics wind tubine design (nd fo the WT pefomnce evlution), developed in pevious wok [5], is bsed on Blde Element Momentum Theoy. In this theoy the bsic ssumption mde is tht the foce of blde element is solely esponsible fo the chnge of momentum of the i

2 which psses though the nnulus swept by the element. It is theefoe to be ssumed tht thee is no dil intection between the flows though contiguous nnuli, condition tht is, stictly, only tue if the xil flow induction fcto does not vy dilly. ppoximtes most closely to the Betz limit vlue of 1/. At lowe tip speed tios the xil flow induction fcto cn be much less thn 1/ nd eofoil ngles of ttck e high leding to stlled conditions. Figue shows tht thee is n incese in Cp in the nge of TSR up to nge of 7 fte which thee is n dmtic decese, whee the mximum Cp is invibly exists between TSR nge of 6 to 8. Figue. 1: Section of Blde Element The component of eodynmic foce on N blde elements esolved in the xil diection is ΩФ +ΩsinФ 1/ ρw Nc(CФ+CsinФ)d The te of chnge of xil momentum of the i pssing though the swept nnulus is ρv α (1- )π dvα 4πρV α (1-) d The dop in wke pessue cused by wke ottion is equl to the incese in dynmic hed, which is ½(ρ Ω) Theefoe the dditionl xil foce on the nnulus is ½(ρ Ω) π d On simplifiction we get, Figue. : Powe Co efficient vs TSR Using these fo the diffeent ifoils of NACA C x, C y is found [9]. Fom these, cn be found nd hence finlly C /C cn be clculted nd theefoe the ifoil with highest C /C tio is identified. III. SEECTION OF AIRFOI The optimiztion of n ifoil is the pio step in the impovement of Cp. The C,C nge fo vious AOA e detemined fom the litetue eview s shown in fig,4,5 fo the selected ifoils on vious AOA..1 Co efficient of dg Gphs fo Re fo the bove sid ifoils is shown hee. In genel, it is notified tht n ifoil with n incesed C nd decesed C esults in bette pefomnce. C Ø + C sinø C x C sinø + C ØC y Finlly the equtions in need fo the clcultion e /(1-) σ /(4sinØ )[C x σ /(4sinØ)C y] /(1+ ) σ Cy / (4sinØØ)whee σ Nc / π Blde solidity σ is defined s totl blde e divided by the oto disc e nd is pimy pmete in detemining oto pefomnce [9]. Chod solidity σ is defined s the totl blde chod length t given dius divided by the cicumfeentil length t tht dius. The mximum efficiency (Cp) occus t tip speed tio, TSR( V tip /V α )fo which the xil flow induction fcto, which in genel vies with dius, Fig. : C fo pofiles fo Re

Fig. 4: C fo pofiles 440-440 fo Re 10405 Fig. 7:C fo pofiles 440-440 fo Re 10405 Tble 1.

3 Fig. 4: C fo pofiles fo Re Fig. 7:C fo pofiles fo Re Tble 1. Ovell compison of mximum C nd minimum C NACA NACA 440- NACA 440- Re C mx C min C mx: C min C mx: C min Fig. 5: C fo pofiles fo Re It is identified fom the bove figues, fo Re 10405, the lowest C Vlue of is seen in NACA 4440(Fig 5) nd the highest C Vlue 1.55 in 4410 (Fig ). Fig,4,5 nlyzed shows fo ll the ifoil C lmost emins unchnged upto AOA 1⁰ whee the devition is seen widely fte C of 0.6. The C vlues fo vious Reynolds numbe 08674, 1980,41749, 51654, fo vious Angle of Attck e dwn fo the ifoils.. Co efficient of g The detemintion of C is shown in the following figues. Fig fo Re fo the ifoils NACA is shown hee. It is identified tht, the C vlue gdully deceses upto C vlue of 0.01nd then inceses pidly. It is infeed fom Fig 6, 7, 8 the low vlues of C e pesent in AOA 0 ⁰ ⁰fo ll the ifoils nd gete devition stts t highe AOA. On the ovell compison, the esults showed NACA 4410 is found to hve the highest C vlue of 1.59 nd NACA 441 is found to hve the lowest C vlue of These vlues e found to be pesent on Re Fo bette esults,the mximum C /C tio ws found which ws pesent on NACA 4410 t AOA 4-5 s Fig 9 shows the cuves when plotted between AOA vs C /C fo diffeent velocities,the cuves ises shply up to AOA 5 nd then deceses whee the mximum devition occus t the sme nge. Fig. 8: AOA vs C /C fo diffeent velocities. IV. OPTIMIZATION OF COEFFICENT OF POWER (Cp) Fig. 6: C fo pofiles fo Re Itetive pocess A cse study of m blde is consideed nd n itetive pocess is cied out nd finlly Cp vlues fo 0, 5 m/s e comped fo convenience. All these wok wee 5

4 cied on NACA 4410 t vious AOA chosen fom 5⁰ to 10⁰. Gluet [1] initited the clcultion of the optimum wind tubine by mking the powe integl eqution sttiony. A pocedue hs been designed fo the itetion pocess whee simple method of compison nd Cp clcultion hs been shown fo two diffeent cses unde exmintion whee C 0 nd Q1 nd othe cse whee C nd Q both e consideed Cse 1(whee C 0 nd Q1) In the itetion pocess, the step 1 tken by the uthos [10, 16] showed, tn ' sin σ C d 4 1 Whee fo convenience futhe with, tn ( 1+ ) ( ) '[ C sin ] σ 4 4 [ C sin ] φ nd step poceeding The itetion pocess is epeted to give n conveged vlue of nd long with, then clculte Cp using the eqution, 8 ( ) d h C 1 P This cse yields n incesed Cp whose defects cn be clculted in the next cse Cse (whee C nd Q e consideed) In this cse it involves the clcultion of the sme pmetes but with the inclusion of C nd Q in them, whee 90 tn 1 1 tn ( 1+ ) ( ) [ C sin + C ] 4Q [ C + C sin ] 4Q Fo the bove sid clcultion whee, [ / R] 1 B / 1 Q exp π ( / R) And Cp finlly clculted by, C P 8 C Q ' tn C h ( ) 1 d When the bove clcultion is cied out fo this cse study, it showed viety of esults fte compison. The mjo design pmetes unde considetion e xil, tngentil induction fcto, inflow ngle, Chod nd Co efficient of pefomnce.. Optimum powe coefficient ws lso investigted by Nthn [14] who deived n ppoximte eltionship between the inflow ngle nd the locl speed tio. The eltion ws given by the following 5th ode polynomil [16]: φ whee ø is mesued in degees. Nthn s eqution ws obtined fo lift-to-dg tio nging fom 8.6 to 66.6 nd the effects of secondy flows in the tip nd hub egions wee not included in the nlysis. A simplified pocedue [16, 17] hs been shown below fo both the cses fo quick esults. It cn lso be simplified in coded fom fo use fiendly wok [ C sin + C ] 4Q [ C sin + C sin ] 4Q And step, 6

5 Stt Ente, R Clculte Clculte γω, C Clculte φ Clculte Ente N Ente V Ente C 1, C Fig. 10: /R vs Axil induction fcto Clculte Poceed until, 1 covege N γ Clculte Q Clculte C p Stop Fig. 11: /R vs Tngentil induction fcto The chod distibution fo m long blde clculted e shown in fig.1. Fig. 10: Flowcht showing Itetive pocess fo n optiml solution. V. RESUTS AN ISCUSSIONS The coefficient of ift nd dg is clculted fo this NACA 4410 seies fo the ngle of ttck 0 to 0. The coefficient of ift inceses with incese in Angle of ttck up to 14 o. Afte 14 o, the coefficient of lift deceses nd stll occus t this ngle of ttck. The lift foce t vious sections fom hub to tip is nlyzed nd it is cleed tht lift foce inceses fom hub to tip fo ll nge of ngle of ttck. The lift foce inceses with incese in ngle of ttck up to 14 o nd it stts to decese fte 14 o. The dg foces begin of dominte beyond this ngle of ttck. The te of incese in lift is moe fo ngle of ttck fom 0 o to 10 o nd between 10 o to 15 o the ise in lift foce is less. But the dg foce inceses with incese in ngle of ttck fom hub to tip. The te of incese in dg incese gdully unlike the te of incese in lift fom 0 o to 16 o of ngle of ttck nd between 10 o to 15 o the ise in lift foce is less. The esults obtined on the cse study (cse )e epesented in gphs below, whee the xil induction fcto nd the tngentil induction fcto deceses exponentilly with incesed /R(Fig 11, 1) t 0 m/s. Fig. 1: /R vs Chod Fig. 1: /R vs Inflow ngle 7

6 Fig. 14: Convegence fo xil induction fcto Fig. 16: Cp vs AOA fo velocity 5 m/s On ovell compison, it is seen fom fig 18, the Cp due to cse 1 is initilly low t lowe velocities whee Cp due to cse is gete, but s velocity inceses, Cp inceses nd becomes gete thn cse. Fig. 14: Convegence fo tngentil induction fcto. The inflow ngle clculted though thee diffeent equtions Gluet eqn, Modified Eqn nd Nthn Eqn e comped s shown in Fig 14.The convegence of nd e shown in the bove fig (Fig 15, 16) whee the itetions convege pidly. Finlly Cp clcultion yielded the shown esults in gphs, on ovell compison of both the velocities t 0m/s nd 5 m/s hs moe Cp on cse 1nsweing the nlyticl clcultions. The figues showing vitions in Cp fo the clculted AOA fo the two diffeent cses fo velocity 0, 5 m/s is shown in Fig 16, 17. Fig. 15: Cp vs AOA fo velocity 0 m/s Fig 16, 17 shows tht fo velocities 0 m/s, 5 m/s Cp is highe fo cse 1 s the tip loss coection fcto, Q is excluded. It is infeed tht the tip loss coection fcto, Q diectly ffects the Cp. Fig. 17: Wind velocity vs Powe co-efficient Hence t lowe velocities, Cp due to cse is gete nd t highe velocities cse 1 is gete due to the impct of tip loss coection fcto. VI. CONCUSIONS In this ppe vious nges of NACA 4 Seies e nlyzed fo diffeent ngle of ttck nd t vious sections.. It is found tht NACA 4410 ifoil t 5 ngle of ttck hs the mximum / tio. The blde with constnt ngle of ttck thoughout the length is nlyzed to find the mximum / tio. This is done t ngle of ttck nging fom -5 to 0 fo the velocity vies fom 5-5 m/sec. The mximum / tio is chieved t 4 of ngle of ttck, fo the vege velocity of 5 m/sec. A cse study of m long blde is consideed, the vitions in xil, tngentil induction fctos nd equtions of inflow e nlyzed. The convegence of the itetive pocess fo xil, tngentil induction fctos povides n optiml solution on two diffeent cses fo the impovement of Cp. At lowe velocities, Cp due to cse 1 is highe nd t highe velocities Cp due to cse is highe s Tip loss coection fcto, Q comes into ply. The mximum Cp chieved is fo velocity 0 m/s t AOA 10⁰ fo cse 1 in this nlysis. The bsic theoies in eodynmics e studied fo futhe optimiztion esults though economic nd efficient nlysis. 8

7 REFERENCES [1] Schmitz G. Theoie und Entwuf von Windden optimle eitsung, Theoy nd design of windwheels with n optimum pefomnce Wiss. Zeitschift de Univesitt Rostock, 5. Jhgng; 1955/56. [] Gsch R, Twele JWind powe plnts,fundmentls, design, constuction nd opetion, Jmes & Jmes Science Publishes td, 00. [] Gluet H.The elements of ifoil nd iscew theoy Cmbidge Univesity Pess, 196. [4] Gsch R, Twele J,Wind powe plnts. Fundmentls, design, constuction nd opetion, Jmes & Jmes Science Publishes td, 00. [5] nzfme R, Messin M,Fluid dynmics wind tubine design: citicl nlysis, optimiztion nd ppliction of BEM theoy, Renewble Enegy Novembe 007; (14): Elsevie Science, ISSN: [6] Gluet H. Aeodynmic theoy, Vol. (IV), ivision, Aiplne popelles, chpte XI, und WF,edito. Belin 195:4 0 (epinted, ove, NY, 196). [7] Gluet H,The elements of eofoil theoy nd iscew theoy,ondon: Cmbidge Univesity Pess,1959. [8] Wilson RE, issmn PBS, Applied eodynmics of wind powe mchines, PB 8595, Repot No. NSF-RA-N-74-11, NTIS, Spingfield, Vigini, [9] Wilson RE, issmn PBS, Wlke SN, Aeodynmic pefomnce of wind tubines, Repot No. NSF/RA-7608, NTIS, Chptes I III, Oegon Stte Univ, June [10] Gnt Ingm,Wind Tubine Blde Anlysis using the Blde Element Momentum Method, Vesion.1. 0, 005. [11] R. nzfme, M. Messin, Hoizontl xis wind tubine woking t mximum powe coefficient continuously, Renewble Enegy 5(010), [1] indenbug C, Investigtion into oto blde eodynmics. ECN-C-0-05, July 00. [1] Nthn GK, A simplified design method nd wind tunnel study of hoizontl-xis windmills, J Wind Engng Industil Aeodynmics 1980; 6: [14] Hnsen MO, ocumenttion of code nd ifoil dt used fo the NRE 10-m wind tubine, ROTABEM-TU, Novembe 000. [15] Km Y. Mlwi, Mhdy T.S. Bdwy,A diect method fo evluting pefomnce of hoizontl xis wind tubines, Renewble nd Sustinble Enegy Reviews 5 (001) [16] K.Y. Mlwi, M.A Bd, A pcticl ppoch fo selecting optimum wind oto,renewble Enegy 8(00),80 8, 008. [17] Wng,. Bi, J. Fletcheb, J. Whitefod,. Cullen, evelopment of smll domestic wind tubine with scoop nd pediction of its nnul powe output, Renewble Enegy, , 008. NOMENCATURE C - ift coefficient. C d - g coefficient. c - Blde chod. V α - Reltive wind velocity Α - Angle of Attck i.e., ngle between i flow incident on the blde nd the blde chod line. - ift foce (Foce cting pependicul to the wind velocity) - g foce(foce cting pllel to the wind velocity) A - Axil flow induction fcto. - Tngentil flow induction fcto. Ø - Wind-speed diection chnge Σ -Roto solidity 9

This immediately suggests an inverse-square law for a "piece" of current along the line.

This immediately suggests an inverse-square law for a piece of current along the line. Electomgnetic Theoy (EMT) Pof Rui, UNC Asheville, doctophys on YouTube Chpte T Notes The iot-svt Lw T nvese-sque Lw fo Mgnetism Compe the mgnitude of the electic field t distnce wy fom n infinite line