CALCULATION OF AERODYNAMICAL EFFICIENCY AND OF THE POWER AT THE LEVEL OF THE BLADES AND THE AXLE OF THE WIND TURBINE

Transcription

1 Analele Universiăţii din Oradea, Fascicula roecţia Mediului Vol. XVI, 2011 ALULATION OF AERODYNAMIAL EFFIIENY AND OF THE OWER AT THE LEVEL OF THE BLADES AND THE AXLE OF THE WIND TURBINE Dubău ălin * *Universiy of Oradea, Faculy of Environmenal roecion, 26 Gen. Magheru S., Oradea; Romania, calin_dubau@yahoo.com Absrac This paper oulines he calculaion of aerodynamical and average efficiency of he wind urbine, as well as he calculaion of powers a he level of he blades and he axle of he urbine. We make an assessmen of he urbine performances based on calculaions of he geomery of he blade profile. The values used in he mahemaical calculaion have been aken from he design calculaions of he urbine. Key words: wind urbine, aerodynamical efficiency, power a he axle of he urbine, power a he level of he blades., INTRODUTION In order o make an appreciaion, in erms of energy, of he performances of he urbine, based on he calculaions characerisic of he geomery of he blade profile, we calculae he aerodynamical efficiency and he average efficiency, as well as he calculaion of power a he level of he blades and he axle. The power a he axle axle is a chief componen of he wind sysems and is yielded by he muliplicaion of he power absorbed by he urbine and is aerodynamical efficiency. Taking ino consideraion ha he wind urbine is inegraed ino a srucure ha is supposed o urn wind power o accoun, i is necessary o menion he level of power for which he calculaions are made. MATERIAL AND METHODS 1. The calculaion of he aerodynamical efficiency: g θ Rand = 1 g β 2. The calculaion of he average efficiency: ( Δ Rand) Rand mediu = ( ) We have used he values deermined from he kinemaical calculaion of urbine design, where he values used have been aken from a varian which was chosen as soluion. 315

2 3. The calculaion ofpower a he level of he blades: paleaj = ( ) ηaerod The values used for he calculaion of power in blades( paleaj) are( ) = 8723,03, and he values for he aerodynamical efficiency have been previously deermined. 4. The calculaion of power a he axle: = paleaj pm (z = 5/6) This relaion describes he power a he axle, where paleaj has been previously deermined, and he mechanically los power ( pm ) depends on he power los in he bearings and he loss in he disc. pm = pd + pl 5. The calculaion of efficiency a he level of he axle: arb Rand arb = ( ) RESULTS AND DISUSSION 1) The calculaion of he aerodynamical efficiency: a) Aerodynamical efficiency (z=5/6) ΔT Rand = ΔT ysin β = y cos β sin β x x = 1 g β x g θ = gθ Rand = 1 g β y Obs.: Values x and y, respecively angleβ, which have been used in he calculaion of efficiency, have beed deermined analyically in he design calculaions of he urbine. y 0,990 0,986 0,982 0,977 0,972 0,967 0,966 0,992 0,990 0,987 0,982 0,979 0,975 0,975 Through he inserion of hese resuls, because of he variaion of he profile ype along he blade, we obain he following values of he aerodynamical efficiency: effic aerod 0,990 0,986 0,982 0,977 0,979 0,975 0,

3 2. The calculaion of average efficiency: b) Average efficiency (z=5/6) For he calculaion of he average efficiency we have used he values deermined hrough he kinemaical calculaion from he varian chosen as soluion, where he calculaion values are as follows: Δ = f (r) 103,22 569, , , , ,51 345,84 ( ) = 8723,03; Effic. are he values deermined above under a) ( Δ Rand) Randmediu = ( ) 0,975 0,980 Obs.: Because of he variaion of he profile ype along he blade we can make a mediaion of he average efficiency as one single final value: effic aver = 0, alculaion of power a he level of he blades: c) alculaion of power paleaj = ( ) η aerod The values used for he calculaion of power a he level of he blades ( paleaj) are as follows: ( ) = 8723,03, and he values for he aerodynamical efficiency have been previously deermined. The resuls can be seen in he following able: 8634, , , , , , , , , , , , , ,97 Through he inserion of hese resuls, because of he variaion of he profile ype along he blade, we obain he following values of power a he level of he blades: paleaj 8634, , , , , , ,97 4. alculaion of power a he axle: d) alculaion of he power a he axle = (z = 5/6) ; paleaj pm 317

4 This relaion describes he power a he axle, where paleaj has been previously deermined, and he mechanically los power ( pm ) depends on he power los in he bearings and he loss in he disc. The mahemaical formulae for he calculaion of he mechanically los power are presened in he following relaions: = + pm pd pl pd = M ω; where d disc l bearing 2 R M = M ρ ω 2 M = 0,01 ρ = 1,225 kg/m 3 2πn n = 250 ro/min ; ω = [rad/s] 60 R = 0,23 m 5 We obain power loss in he disc value pd = 0, 0027, where he values used in he mahemaical calculaions have been aken from he design calculaion of he urbine. pl = M f r ω; where 2πn ω = [rad/s]; n = 250 ro/min 60 G = m g Ff r M r = μ m g = μ m g f r 1 where g = 9,81 m/s 2 ; m = 545 kg; μ = 0,01; r 1 = 0,14 m; ower loss in he bearings has he calculaion value pl = 195, 957. The values used in he mahemaical calculaion have been aken from he design calculaions of he urbine. Finally, we obain he following values for he mechanically los power: pm = 0, ,957 = 195,96 paleaj = : pm 318

5 8438, , , , , , , , , , , , , ,01 Through he inserion of hese resuls, because of he variaion of he profile ype along he blade, we obain he following values of power a he level of he axle: 8438, , , , , , ,01 5. alculaion of efficiency a he axle of he urbine: = paleaj pm Finally, he calculaion of efficiency a he axle of he urbine is yielded hrough he relaion: arb Rand arb = ( ) Effic blades : 0,967 0,964 0,960 0,955 0,950 0,945 0,944 0,970 0,967 0,964 0,960 0,956 0,953 0,952 Through he inserion of hese resuls, because of he variaion of he profile ype along he blade, we obain he following values of power a he level of he axle: Effic blad 0,967 0,964 0,960 0,955 0,956 0,953 0,952 ONLUSIONS 1. Following his calculaion, because of he variaion of he profile ype along he blade, we obain he following values of he aerodynamical efficiency: effic aerod 0,990 0,986 0,982 0,977 0,979 0,975 0, Because of he variaion of he profile ype along he blade we can make a mediaion of he average efficiency as one single final value: effic aver = 0, Because of he variaion of he profile ype along he blade, we obain he following values of power a he level of he blades: 319

6 paleaj 8634, , , , , , ,97 4. Through he inserion of hese resuls, because of he variaion of he profile ype along he blade, we obain he following values of power a he level of he axle: 8438, , , , , , ,01 5. Through he inserion of hese resuls, because of he variaion of he profile ype along he blade, we obain he following values of efficiency a he level of he axle: Rand arb 0,967 0,964 0,960 0,955 0,956 0,953 0,952 I can be noiced ha we have obained elevaed values of efficiency, boh aerodynamically and a he level of he axle of he urbine, values which are similar o he resuls published inernaionally. REFERENES 1. Bej A., 2003, Turbine de vân, olecţia Energeica Ediura oliehnica Timişoara, ISBN , Dubău., 2007, Uilizarea microagregaelor eoliene în componenţa unor siseme complexe, Ediura oliehnica Timişoara, ISSN: , ISBN: , Gyulai F., 2000, urs de specializare în ehnologii energeice durabile. Modulele: Insalaţii Eoliene şi Agregae Eoliene, Gyulai F., 2003, onribuions on horizonal axis wind urbine heory, A V-a onferinţă Inernaţională de Maşini Hidraulice şi Hidrodinamică, oc. 2000, Timişoara, România, Gyulai F., 2003, Vocaional Traning in Susainable Energy-ourse Wind Energy, Gyulai F., A. Bej., 2000, Sae of Wind Turbines in he End of 20h enury and roposals for Romanian Opions, Buleinul Şinţific al Universiăţii oliehnica, Timişoara, România, Tom 45(59), 2000-ISSN, , Gyulai F., 1992, Ecological argumens foe he Wind Farrn Semenic, SDWE Timisoara, 8. Harison E., 1989, Sudy on he nex generaion of large wind urbines, EWE. 9. Ilie V., Almaşi L., Nedelcu Ş., 1984, Uilizarea energiei vânului, Ediura ehnică Bucureşi, Spera D. A., 1994, Wind urbine echnology Fundamenal conceps of wind urbine engineering, ASME RESS, New York 320