Iteratioal Sietifi Joural Joural of Evirometal Siee http://eviromet.sietifi-joural.om/ Optimizatio desig i Wid Turbie Blade Based o Speifi Wid Charateristis Yuqiao Zheg College of Mehao-Eletroi Egieerig Lazhou Uiv. of Teh.Chia Lazhou, Chia zhegyuqiao@sohu.om Yogyog Cao College of Mehao-Eletroi Egieerig Lazhou Uiv. of Teh.Chia Lazhou, Chia aoyy_5794@63.om Rogzhe Zhao College of Mehao-Eletroi Egieerig Lazhou Uiv. of Teh.Chia Lazhou, Chia zhaorogzhe@lut. Abstrat The highest possible power output uder speified atmospheri oditios plays a ey role i desigig a wid turbie blade, i this paper, the maximum lielihood estimatio method was used to ompute the hub height wid speed (65m)mathematial model based o the observatio data of Hexi Corridor wid at m height, taig 4m blade as a example, the model is established by Blade Elemet Mometum Theory, at the same time the tip loss is taig ito aout, eah setio of the hord, twist agle of wid eergy utilizatio oeffiiet, si ply ad girder ap layer thiess parameters were optimized, the aerodyami performae ad stress distributio are give out, the results showed that the optimized: the optimized blade wid eergy utilizatio oeffiiet is greatly improved ad the quality of the blade is redued sigifiatly, it is suitable for wid harateristis of the blade desig oditio performae supper tha that of geeral blade, it provides a theoretial basis for the blade desig. Keywords the wid; maximum lielihood estimatio; aerodyami performae; wid eergy utilizatio oeffiiet optimizatio model I. INTRODUCTION Blade is oe of the ey ompoets i the wid turbie. The wid turbie a trasfer wid eergy to mehaial eergy i a rotor osistig of two or more blades ad hub. Blade plays a ey role i the safe operatio of wid turbie. Whe desigig reliable quality ad superior performae blade, the atual operatio status of wid turbie must be tae ito aout. The regioal desig ad researh of blade is the future developmet tred [-].Curretly, the blade desig speifiatios are maily based o iteratioal stadard IEC64-, Germay (GL rules), ad the relevat wid power stadards i Chia [3-4]. However, the wid resoures situatio is differet betwee Chia ad other outries. Whe seletig wid speed model, we usually referee the wid observatio height of weather statio whih is m, however, the istallatio height of wid turbie hub is 5m to 7m, or eve higher. This leads to the iput soure of load a ot meet the requiremets of some software ad mae the result of wid load alulatio iauray. The Hexi orridor whih loated i the orthwest of Chia is the uique wid resoure aumulatio zoe i Chia or eve all over the world, ad the wid resoures of Hexi have its ow This projet is supported by Natioal Natural Siee Foudatio of Chia (Grat No. 55658) ad LaZhou Tehology Developmet Program o f Chia(Grat No. 4--75 ) geographi features. There are oly two types of wid the east wid ad the west wid i Hexi orridor, so the wid turbie blade ru i the frequet hagig yaw agle situatio. This seriously affets the reliability of wid turbie operatio [5]. The reports of how to apply iteratioal stadard to alulate regioal wid resoure harateristis ad the regioal desig of blade are few i Chia. So the desig of wid turbie blade i speifi situatio is oe of problems that egieerig appliatio ad researh urget to solve [6-7].The wid turbie blade optimizatio desig method whih based o wid harateristis i Hexi area is preseted i this paper based o a aerodyami theory. This method taes wid eergy utilizatio oeffiiet ad girder struture parameters as the optimizatio goal, ad through the geeti algorithm to ostrut the whole blade optimal solutio. The get the blade optimal solutio with better peumati ad struture performae. Providig a referee for optimizatio ad desig of regioal high-performae blade. II. WIND SPEED MODEL The harateristis of wid are radomess flutuatio ad itermittet. Whe evaluatig wid resoures at a ertai area ot oly deped o wid speed data, but also should master its stable statistial features i a log time. The probability distributio of wid speed is a importat form of wid statistial properties. There are a lot of wid speed fittig models of probability distributio of wid speed, but amog them two-parameter Weibull ad Rayleigh distributio are widely osidered to be a powerful tool to desribe wid speed statistial properties[8]. Whe usig two-parameter Weibull model to fit the wid speed distributio, the probability desity futio a be expressed as: v v f() v = exp () Where: v is wid speed f(v) is the appearae probability of wid speed v is shape parameter, dimesioless
is sale parameter Where : ( ) Γ is the Gamma futio. v = Γ () x t x = t e dt Γ ( ) (3) Whe =, wid speed distributio is stadard Weibull distributio. Whe <<, the mode of distributio is, f(v)is the dereasig futio of wid speed v. Whe =, f(v) beomes expoetial distributio. Whe =3.5, f(v) very lose to ormal distributio. The bigger the, shows that the smaller hage of the average wid speed i a ertai period of time; the smaller the, shows that the bigger hage of wid speed rage. Partiularly, whe =, the distributio is speifially ow as Rayleigh distributio, there is oly oe parameter i it; the wid speed probability desity futio a be expressed as: v v f() v = exp A. Parameter Estimatio Method I order to establish mathematial model of wid speed of harateristis of regioal wid resoures, we must solve the problem of high auray parameter estimatio. Weibull distributio is a ommo futio of wid speed distributio of wid field. There is a lot of methods to alulate the parameter ad i Weibull model; we use maximum lielihood estimatio method [9-] to alulate the shape parameter ad the sale parameter i Weibull model i this paper. Aordig to the Weibull probability desity futio of wid speed distributio, struture maximum lielihood futio as follows: vi vi L(, ) = f( vi ) = exp i= i= The atural logarithm of above formula a be expressed as: Iteratioal Sietifi Joural Joural of Evirometal Siee http://eviromet.sietifi-joural.om/ (4) (5) ( ) H, v v H = = + v = i= H Where: (, ) i i l( i ) l l (7) H vi = = = i= vi l vi l vi i= i= = vi i= = i= v i ( ) B. Wid Speed Distributio at the Height of Hub (8) (9) () Whe aalyzig the harateristis of the wid eergy resoures, it is diffiult to ifer the harateristis of wid eergy resoures aurately at the height of hub (65m) aordig to the wid eergy resoures at the height of m. May areas la of measured data of wid speed of differet height; so we usually use log-term observatio data of wid at the height of m whe alulatio, the auray of result is ot high. Therefore, it is eessary to mae the statistial result [5] of wid eergy resoures at m outward expasio to the height of hub (65m) i Hexi regio. Whe aalyzig wid speed distributio at 65m, we get the wid speed data at 65m whih alulated from data of wid speed at the stadard height by usig formula (4), the use maximum lielihood estimatio method to get the wid speed probability desity futio whih is show i Fig.. P rob ab ility d e sity futio..8.6.4.. 3 W i d sp e ed (m /s) E x tr ap o la ted data W eib u ll W -M L E Fig. Wid Speed Probability Desity Futio at the Height of Hub vi H(, ) = l [ L(, ) ] = ( ) l( vi ) + l l i= (6) The maximum lielihood estimate of ad (i the above equatio) a be obtaied by solvig equatio (5) ad (6). III. CALCULATION OF BLADE AERODYNAMIC PARAMETER Wid turbie blade aerodyami performae is determied by the power, thrust, torque ad its orrespodig oeffiiet [-].Whe alulatig the aerodyami performae, firstly, the axial iduible fator a ad irumferetial iduible fator b are alulated aordig to mometum blade elemet theory; Seodly, the air veloity triagle of blade elemet ad the ormal fore df ad tagetial fore df t that effet o blade elemet are
Iteratioal Sietifi Joural Joural of Evirometal Siee http://eviromet.sietifi-joural.om/ obtaied; Thirdly, axial fore dt ad torque dm whih effet o eah blade elemet are alulated too; Fially, alog the blade spawise itegratio, the axial fore T, torque M ad shaft power P that effet o whole turbie are also alulated. Lift fore ad resistae are show i figure : IV. SAMPLE ANALYSIS The ow oditios: blade legth 4m; airfoil profile NACA63-XXX series; rated wid speed m/s; ut-i wid speed 3m/s;ut-out wid speed 5/s(miutes mea value).use geeti algorithm to optimize the alulatio(taig hord legth, torsioal agle, frot layer thiess as the desig variables ad taig wid eergy utilizatio oeffiiet ad girder struture parameters as the optimizatio goal). TABLE. BLADE DESIGN BASIC PARAMETERS Fig. Figure of Lift Fore ad Resistae siφ φ F = ; C = ; a = l d C = π a Axial iduible fator alulatio amedmet is: ' 4 4 ' (8 ' r r ) a = + π σ + π σ β + πσ 4 () () Iitializig iduible fator a ad b, the axial iduible fator that alulated by iitial value a redue iteratio time. I flow agle is [3]: Where: Agle of atta is: C T ( ) ta φ U a = Ωr( aʹ) (3) a = φ β (4) σʹ( a) ( Clos φ+ Cd si φ) = (5) si φ Beause the fore o blade elemet whih at the tip of blade have exerted a far-reahig ifluee o the aerodyami performae of whole wid turbie blade, so the tip loss should ot be igored. If osiderig the Pradtl tip loss orretio fator, tip loss oeffiiet F a be defied as: B ( R r) F = aros exp π Rsiϕ (6) The, the otributio that eah blade elemet otribute to total wid eergy utilizatio oeffiiet is: 8 3 dcp = b( a) F d (7) Rated power 5 KW blade legth The rated Speed at the Height of Hub The rated Wide speed 4.5m 7.m/s 65m 8.5 m/s The hord legth distributio (before ad after optimizatio) is show i Fig.3.The optimized blade hord legth distributio alog the spawise preset a oliear harateristis whih a be see from the figure o the whole, eah hord legth of blade elemet is greater tha the iitial blade, ad the optimized blade hord legth distributio is more smooth espeially at the middle of the blade. However, the hord legth of blade root ad blade tip less tha the iitial blade; this is beause it develops toward to the tred of ireasig blade area i the optimizatio proess (osiderig wid resoure harateristis of Hexi i alulatio ad taig maximum wid eergy utilizatio oeffiiet as the objetive futio). hord distributio m 3.5 3..5 iitial value optimal value..5..5. 3 4 blade radius (m) Fig. 3 Compariso of Chord legth Optimizatio The torsioal agle distributio after optimizatio is show i Fig.4.We a see from the piture, torsioal agle distributio presets oliear harateristis, ad the etirety has the tred of ireasig uder the oditio of torsioal agle optimal value rigidity. The torsioal agle value reah the maximum at r/r=. after optimizatio, however its maximum value at r/r=.5 before optimizatio. The maximum value of optimized blade torsioal agle is more lose to the blade root, ad the distributio of torsioal agle is more smooth. The mai reaso leads to irease hord legth of blade root is the torsioal agle of blade root is greater tha iitial blade whih osider the regioal wid load effets, ad it beefits to redue the load of blade root, the irease the servie life of blade.
Iteratioal Sietifi Joural Joural of Evirometal Siee http://eviromet.sietifi-joural.om/ twist distributio dgree Fig. 4 Torsioal Agle Optimizatio We a see from figure 5, low wid speed area torque oeffiiet delied slightly, ad high wid speed torque oeffiiet ireased after optimizatio. It illustrates that probability of ourree of wid speed is bigger at high wid speed area, so we a improve the high wid speed area wid eergy utilizatio. The optimized wid turbie blade uder the oditio of low wid speed, wid rotor is able to obtai large torque. So wid turbie a reah the rated speed faster, the ireases its aual eletriity output. C m Fig. 5 C M Charateristi urve Curve of thrust oeffiiet hagig with blade tip speed (before ad after optimizatio) is show i figure 6. We a see from the figure, wid rotor thrust oeffiiet ireases with the ireases of blade tip speed, it meas that the axial thrust that wid rotor effeted ireases with the ireases of blade tip speed. The thrust o optimized blade slightly smaller tha the origial wid rotor thrust whe tip speed ratio (high wid speed) at the rage of 4 to 7.5, ad it is beefiial to redue the whole wid turbie load. Whe wid turbie operatio (tip speed ratio greater tha 8.5), the thrust oeffiiet ireased sigifiatly after optimizatio. But this does ot substatially ireases the whole wid turbie load, ad wid turbie a redue the load through varyig propeller, stallig ad other measures. C t 5 5..8.6.4.5..5..5 C t iitial value C t orretio value C m iitial value iitial value optimal value -5 3 4 blade radius (m) C m orretio value. 3 4 5 6 7 8 9 34 Curve of power oeffiiet hagig with blade tip speed ratio (before ad after optimizatio) is show i figure7. We a see that the power oeffiiet is sigifiatly greater tha the iitial blade whe tip speed ratio at the rage of 6 to, ad this is maily aused by differet blade shape parameters. Blade has the highest wid eergy utilizatio oeffiiet whe tip speed ratio at the rage of 8 to (before optimizatio), ad its maximum value is.485. Moreover, the maximum value of wid eergy utilizatio oeffiiet is.4, ad the Betz limit is.593; there is a big gap betwee them. The reaso of it is that the wid eergy utilizatio at blade root is ot high whe alulatig wid eergy utilizatio oeffiiet of blade. The wid eergy utilizatio maily oetrated at.r to R alog the spawise, that is shows the rage of wid eergy utilizatio of blade is wider after optimizatio, the aerodyami performae of blade improved, ad its aerodyami effiiey is higher. Fig.7 C P- Charateristi urve The power urve of wid rotor overall hage is small whe usig wid speed distributio at m ad 65m respetively, we a see it from figure 8. Wid rotor power slightly more tha m height observatio data whe wid rotor at the height of hub ad wid speed v<m/s; wid rotor power was ostat at.5mw whe wid speed v>m/s, this is beause whe wid turbie reahed rated wid speed, it uses measure of adjustig pith agle to esure ostat output, the osistet with atual operatio power. Power (w) C p.5.4.3... 3 4 5 6 7 8 9 34.x 6.75x 6.5x 6.5x 6.x 6 7.5x 5 5.x 5.5x 5 C p iitial value C p orretio value ase ase. 5 5 5 Wid speed (m/s).. 3 4 5 6 7 8 9 34 Fig. 6 C T- Charateristi urve Fig. 8 power ompariso (before ad after optimizatio) Aerodyami fore diretly affets the layer struture of the blade. Mai girder ap layer thiess distributio uder
Iteratioal Sietifi Joural Joural of Evirometal Siee http://eviromet.sietifi-joural.om/ differet wid speed (at the height of m ad 65m) is show i figure 9. We a see from the figure that the mai girder ap layer thiess distributio presets oliear harateristis; the mai girder ap layer that use atual wid load to alulate at the height of 65m is ireased ear blade root uder rigid oditio. Blade girder is the mai bearig part, the optimized girder ap layer thiess dereases at.r-.5r, ad girder ap layer thiess ireases to satisfy the requiremet of blade overall rigidity at /-R. beam layer thiess m.8.7.6.5.4.3... 3 4 blade radius (m) Fig. 9girder ap layer thiess ompariso (before ad after optimizatio) Curve of blade mass liear desity uder wid load ifluee of two worig oditios is show i Figure. The figure shows that the optimized blade setio mass liear desity dereases ear blade root. However, blade root is the aumulatio area of blade mass; so this redue blade overall mass, ad redue the blade maufaturig ost. Fig. stress distributio Further, blade stress is aalyzed. Through aalyzig figure, blade mai bedig strai zoe is loated at girder whih is loated at /3-/3 of blade alog the spawise, blade stress is big at the part of girder ap, ad its miimum value is loated ear the blade tip. So hagig the girder ap layer is oe of the most effetive measures to improve blade stress, ad its maximum stress at blade root oform to the GL stadard. Therefore, stress aalysis result that uder the regioal wid resoures harateristis is believable. V. CONCLUSIONS iitial value optimal value Based o harateristis of the wid resoure i Hexi area, optimizatio researh ad desig of blade whih adapt to the wid resoure harateristis flexibly is arried out, ad get the followig olusios by aalyzig the optimizatio results: a) I this paper, based o m level log-term observatio data of wid speed i Hexi orridor, use maximum lielihood estimatio to establish mathematial model at the height of hub i Hexi orridor, ad alulate the shape parameter ad sale parameter of Weibull model, the provide a theoretial basis for the aurate model of wid speed of regioal wid resoures harateristis. b) Based o the theory of blade elemet mometum, the aerodyami mathematial model is established. The hord legth torsioal agle ad thrust oeffiiet of eah blade elemet are greatly improved, ad the quality of blade is sigifiatly redued after optimizatio. The hord legth ad torsioal agle at blade root do ot appear extremely distortio of geometri shape. The hord legth of blade root ad blade tip are less tha iitial blade, the maximum torsioal agle is loser to the blade root, ad the distributio of the torsioal agle is more smooth after optimizatio. All these above will brig great oveiee to blade produtio ad blade maufaturig proess; Whe tip speed ratio at the rage of 4-7.5, the thrust o blade dereases, the the load o wid turbie dereases. ) Based o the alulatio of aerodyami fore, the blade, si layer, ad mai girder ap layer thiess are optimized. Compared with iitial blade, the optimized blade torsioal agle at blade root is sigifiatly greater tha the iitial blade, ad this will redues the load of blade root, the ireases the servie life of blade. Fially, the stress aalysis of optimized blade is doe, ad the mai stress positio of blade is poited out. The researh of this paper provides importat guidig sigifiae for subsequet wid turbie blade struture desig ad optimizatio. REFERENCES [] Dai Juhua, prof liu. Large wid turbie blades researh status ad developmet tred[j]. Joural of mehaial egieerig, 3, 49(): 4-43 [] Islam M R, Mehilef S, Saidur R. Progress ad reet treds of wid eergy tehology[j]. Reewable ad Sustaiable Eergy Reviews 3, (): 456-88. [3] Zheg We-jua, Huag Shou-dao,Gao Jia. A aalyti eletromageti alulatio method for performae evolutio of doubly fed idutio geerators for wid turbies[j]. Joural of Cetral South Uiversity of Tehology, : 763 774. [4] Katar YM, Usta I. Aalysis of wid speed distributios: Wid distributio futio derived from miimum ross etropy priiples as better alterative to Weibull futio [J]. Eergy Coversio ad Maagemet, 8, 49(5): 96-973. [5] Zhu Biao, huhua, Ma Peg et. Wid speed hage tred aalysis, gasu provie [J]. Joural of resoures ad eviromet i arid areas,, 6(): 9-95. [6] Li Wag, Liaggag Guo, Nathalie ReevierA mathematial model for alulatig ross-setioal properties of moder wid turbie omposite blades. [J]. Reewable Eergy, 64 (4) 5-6. [7] Mai K, Sbragio R, Vlahopoulos N. System desig of a wid turbie usig a multi-level optimizatio approah [J]. Reewable Eergy, 43: -4. [8] Apir E K. A assessmet o seasoal aalysis of wid eergy harateristis ad wid turbie harateristis [J].Eergy Coversio ad Maagemet, 5, 46(-): 848-867.
[9] Dorval A.Estimatig wid speed distributio[j]. Eergy Coversio ad Maagemet,, 43(7): 3-38. [] Katar YM, Usta I. Aalysis of wid speed distributios: Wid distributio futio derived from miimum ross etropy priiples as better alterative to Weibull futio[j]. Eergy Coversio ad Maagemet. 8, 49(5): 96-93. [] Morales, A, W ahter, M, ad Peie, J, Charaterizatio of wid turbulee by higher order statistis[j]. Wid Eergy,, 5(3): 39-46. [] P. Fuglsag, H.A. Madse. Optimizatio method for wid turbie rotors [J]. Joural of Wid Egieerig ad Idustrial Aerodyamis,, 8(7): 9-6. [3] Weifei Hua, Dohyu Par. Strutural optimizatio proedure of a omposite wid turbie blade for reduig both material ost ad blade Weight [J]. Egieerig Optimizatio, 3, 45:, 469-48. Iteratioal Sietifi Joural Joural of Evirometal Siee http://eviromet.sietifi-joural.om/