Investigation of blade performance of horizontal axis wind turbine based on blade element momentum theory (BEMT) using NACA airfoils

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1 MultiCaft Intenational Jounal of Engineeing, Science and Technology Vol., No. 1, 010, pp INTERNATIONAL JOURNAL OF ENGINEERING, SCIENCE AND TECHNOLOGY MultiCaft Limited. All ights eseved Investigation of blade pefomance of hoizontal axis wind tubine based on blade element momentum theoy (BEMT) using NACA aifoils Nitin Tenguia 1, N.D. Mittal 1, Siaj Ahmed 1 Depatment of Applied Mechanics, Maulana Azad National Institute of Technology, Bhopal, INDIA Depatment of Mechanical Engineeing, Maulana Azad National Institute of Technology, Bhopal, INDIA Coesponding Autho: nitintenguia@yahoo.co.in, Tel Abstact The basic pinciple of wind tubine conveting wind enegy into electicity comes fom the lift poduced by the ai flowing though the oto. The shape of oto blade plays an impotant ole in detemining the oveall aeodynamic pefomance of a hoizontal axis wind tubine. In this wok, blade is designed fo a 5KW hoizontal axis wind tubine which is aleady in maket. Fo designing blade, blade element momentum theoy (BEMT) is used and a compute pogam is developed to automate the complete pocedue. Two NACA aifoils ae taken fo the compaative calculation of elemental powe coefficient and othe paametes such as chod, thickness and twist distibution. The aifoil taken fo designing the blade is same fom oot to tip. Stesses ae maximum at the blade oot. In this wok, the blade oot is thickest potion of the blade and twist is maintained such that the angle of attack will be maximum at evey station of the blade. In the designed blade, the elemental powe coefficient is maximum in tansition segment. The pesent method is useful fo pedicting the pefomance of wind tubine blade. Keywods: Powe coefficient, Twist, Chod, Aifoil, Design. 1. Intoduction The powe efficiency of wind enegy systems has a high impact in the economic analysis of this kind of enewable enegies. The efficiency in these systems depends on many subsystems: blades, geabox, electic geneato and contol. Some factos involved in blade efficiency ae the wind featues, like its pobabilistic distibution, the mechanical inteaction of blade with the electic geneato, and the stategies dealing with pitch and otational speed contol. It is a complex poblem involving many factos, elations and constaints. The inceasing awaeness of the geneal public to climate change and global waming has povided oppotunities fo wind tubine applications in the UK. The UK claims 40% of the wind enegy esouces of Euope. Study of Ackemann, (00) shows Euope leads the wold with 70.3% (3GW peak) of the total opeational wind powe capacity wold wide. As well as lage wind tubines opeating in open aeas on- and off-shoe, moe small-scale wind tubines ae being installed and opeated by homeownes and small entepises. One of the diffeences between lage- and small-scale wind tubines is that small-scale wind tubines ae geneally located whee the powe is equied, often within a built envionment, athe than whee the wind is most favoable. In such location, the wind is nomally weak, tubulent and unstable in tems of diection and speed, because of the pesence of buildings and othe adjacent obstuctions. To yield a easonable powe output fom a small-scale wind tubine located in this tubulent envionment, and to justify such an installation economically, the tubines have to impove thei enegy captue, paticulaly at low wind speeds and be esponsive to changes in wind diection. This means that small-scale tubines need to be specifically designed to wok effectively in low and tubulent wind esouce aeas. Accoding to Spea, (1994) the Glauet and Wilson methods wee mostly used fo blade design. The objectives of these methods wee to obtain the maximum powe coefficient of each blade section at the design wind speed. Because the time vaiation chaacteistics of wind speed ae not taken into account, blades designed by these methods cannot achieve the maximum annual enegy output. Futhemoe, design esults fom these methods must be substantially amended to get smooth chod length and twist

2 6 Tenguia et al. / Intenational Jounal of Engineeing, Science and Technology, Vol., No. 1, 010, pp distibutions. Because the amended esults aleady deviate fom the design points, effectively contolling design esults pose poblems. A esent study by Maalawi et al, (001) has indicated that the theoetical optimum distibution of the inflow angle can be adequately detemined fom an exact tigonometic function method, which is based on Glauet s, (1935) optimum condition. The developed appoach eliminated much of the numeical effots as equied by the othe iteative pocedues, and a unique elation in the angle of attack was developed, ensuing convegence of the attained solutions. A pototype 3 kw hoizontal upwind type wind tubine geneato of 4 m in diamete has been designed by Nagai et al. (009) and examined unde eal wind conditions. The machine was designed based on the concept that even small wind tubines should have a vaiable pitch contol system just as lage wind tubines, especially in Japan whee typhoons occu at least once a yea. A chaacteistic of the machine is the use of a wom and gea system with a stepping moto installed in the cente of the hub, and the otational main shaft. The machine is constucted with no mechanical beaking system so as to avoid damage fom stong wind. In a stom, the wind tubine is slowed down by adjusting the pitch angle and the maximum electical load. Usually, the machine is contolled at seveal stages depending on the otational speed of the blades. Two contol methods have been applied: the vaiable pitch angle, and egulation of the geneato field cuent. The chaacteistics of the geneato unde each otational speed and field cuent ae fist investigated in the laboatoy. This pape descibes the pefomances of the wind tubine in tems of the functions of wind tubine otational speed, geneated outputs, and its stability fo wind speed changes. The expected pefomances of the machine have been confimed unde eal wind conditions and compaed with numeical simulation esults. The wind tubine showed a powe coefficient of 0.57 unde the aveage wind speed of 7.3 m/s. An optimization model pesented by Liu et al. (007) fo hoizontal axis wind tubine. The model efes to the wind speed distibution function on the specific wind site, with an objective to satisfy the maximum annual enegy output. To speedup the eseach pocess and guaantee a global optimal esult, the extended compact genetic algoithm (ECGA) is used to cay out the seach pocess. Compaed with simple genetic algoithm, ECGA uns much faste and can get moe accuate esults with a much smalle population size and fewe function evaluations. Using the developed optimization pogam, blades of 1.3 MW stall egulated wind tubine ae designed. Compaed with the existing blades, the designed blades have obviously bette aeodynamic pefomance. The design and selection pocedue of aifoil sections fo small wind tubine blades is discussed and implemented by Habali, (1995). It is found that fo blades up to 5 m. long, two diffeent aifoils mixed at the oute thid of the span will be sufficient and have demonstated good stength and aeodynamic chaacteistics. A mathematical model fo fluid dynamics wind tubine design by Lanzafame et al., (007) (based on blade element momentum theoy) has been implemented and impoved. The mathematical simulations have been compaed with expeimental data found in liteatue. The simulation was pefomed fo the whole wind velocity ange, in on-design and off-design conditions. Seveal simulations wee pefomed in ode to maximize the ageement between the simulated and expeimental data. Paticula attention was paid to the tangential induction facto and to the models fo the epesentation of the lift and dag coefficients. Seveal eseaches have contibuted to the insight into oto design. Snel (1998, 003) descibe wind tubine aeodynamics in geneal and gives an oveview of the available methods to compute the aeodynamic oto pefomance. Fuglsang, (00) descibes the methods needed in the oto design pocess in tems of a guideline and Tangle, (000) gives a shot histoical oveview of the oto design investigations. Also, aeodynamic optimization of otos is descibed by Fuglsang, (1999) Giguee, (000) Nygaad, (1999) espectively. Details in oto design to incease the powe efficiency have been investigated by seveal eseaches; Johansen and Madsen (007) investigated especially the oot pat of otos and found that a new oot design of the otos did not incease the powe pefomance significantly. Howeve, the inteaction between diffeent paametes in the oto design, such as Tip- Speed-Ratio, Reynolds numbe etc. still needs to be investigated simultaneously when addessing design of otos with maximum powe pefomance. This pape focuses on pefomance investigation of wind tubine blade fo a 5KW HAWT. This wok is caied out on a commecial available wind tubine manufactued by Qingdao Sea.Silkoad Int'l Co.Ltd. all though this wok, the lift coefficient is taken as 1.1 which is constant thoughout the blade. The lift and dag coefficients ae taken fom Abbott, (1958). These values ae taken fo Reynolds numbe 3 X Unde this investigation, two aifoils ae taken, namely, the fou digits and the five digit aifoil. The blade is divided into ten elements and powe coefficient is calculated fo each element with the help of a compute pogam. Chod and thickness of the blade is maximum at the oot because of stesses and the twist is maximum nea the oot. Figue 1 shows the complete pocess of the wok.. Specification and Aifoil Popeties.1 Specifications Table 1: The specification of wind tubine taken, ae made by Qingdao Sea.Silkoad Int'l Co.Ltd. The capacity of this tubine is 5KW. Model HY-5KW Rated powe(kw) 5 Maximum powe(kw) 5.4

3 7 Tenguia et al. / Intenational Jounal of Engineeing, Science and Technology, Vol., No. 1, 010, pp Table 1 (cont d): The specification of wind tubine taken, ae made by Qingdao Sea.Silkoad Int'l Co.Ltd. The capacity of this tubine is 5KW. Roto Diamete 5.6 Rated voltage(v) DC40V/AC0 Rated wind speed(m/s) 11 Stating Wind speed(m/s) 3 Woking wind speed(m/s) 4-5 Suvived wind speed(m/s) 50 Blades mateials Fibeglass-einfoced plastics Rated otate speed(/min) 40 Speed egulation method Yawing & Electomagnetic bake Geneato style 3-phase AC PM Towe height(m) 6 Stop method By hand main machine weight(kg) 340 Guyed towe weight(kg) 350 Fee standing towe weight(kg) 360 Figue1: Geneal pogam flowchat

4 8 Tenguia et al. / Intenational Jounal of Engineeing, Science and Technology, Vol., No. 1, 010, pp Aifoil Popeties In this wok, two aifoils ae taken, one of them is fou digit and the othe is five digit aifoil. Theoy of wing section by Abbott, (1958) is used fo taking the popeties of aifoils. The selection of aifoil is vey impotant point in designing an efficient oto. Gifith, (1977) showed that the output powe is geatly affected by the aifoil lift-to-dag atio, while Hassanein, (000) ecommended that the aifoil be selected accoding to its location along the blade to ensue its highest contibution to the oveall pefomance. The numbeing system fo NACA wing sections of the fou-digit seies is based on the section geomety. The fist intege indicates the maximum value of the mean-line odinate y c in pe cent of the chod. The second intege indicates the distance fom the leading edge to the location of the maximum cambe in tenths of the chod. The last two integes indicate the section thickness in pe cent of the chod. Thus the NACA 441 wing section has 4 pe cent cambe at 0.4 of the chod fom the leading edge and is 1 pe cent thick. The numbeing system fo wing sections of the NACA five-digit ( ) seies is based on a combination of theoetical aeodynamic chaacteistics and geometic chaacteistics. The fist intege indicates the amount of cambe in tems of the elative magnitude of the design lift coefficient; the design lift coefficient in tenths is thus thee-halves of the fist intege. The second and thid integes togethe indicate the distance fom the leading edge to the location of the maximum cambe; this distance in pe cent of the chod is one-half the numbe epesented by these integes. The last two integes indicate the section thickness in pe cent of the chod. 3. The Blade Element Momentum (BEM) Theoy The basic assumption in blade element momentum theoy is that the foce of the blade element is solely esponsible fo the change of momentum in the ai which passes though the annulus swept by the blade element. It is theefoe to be assumed that thee is no adial inteaction between the flows though contiguous annuli a condition that is stictly only tue if the axial flow induction facto does not vay adially. In pactice, the axial flow induction facto is seldom unifom but expeimental examination of flow though popelle disk by lock (194) shows that the assumption of the adial independence is acceptable. The component of aeodynamic foce on N blade elements esolved in the axial diection is 1 δlcosφ + δdsin φ = ρw Nc( CLcosφ + Cd sin φ) δ (1) The ate of change of axial momentum of the ai passing though the swept annulus is ρv (1 a)πδav = 4 πρv a(1 a) δ () The dop in wake pessue caused by wake otation is equal to the incease in dynamic head, which is 1, ρ ( aω ) Theefoe, the additional axial foce on the annulus is 1 ρ ( a' Ω ) πδ Thus, 1 ρw Nc( Cl cosφ + Cd sin φ) δ = 4 πρ[ V0 a(1 a) + ( a' Ω ) ] δ Simplifying, W c N ( C cos sin ) 8 ( (1 ) ( ' ) ) (3) l φ+ Cd φ = π a a + a λμ μ V0 R The element of axial oto toque caused by aeodynamic foces on the blade elements is 1 ( δlsinφ δdcos φ) = ρw Nc( Cl sinφ Cd cos φ) δ (4) The ate of change of angula momentum of the ai passing though the annulus is ρv0(1 a) Ω a' πδ = 4 πρv0( Ω) a'(1 a) δ (5) Equating the two moments 1 ρw Nc( Cl sinφ Cd cos φ) δ = 4 πρv0 ( Ω) a'(1 a) δ (6) Simplifying,

5 9 Tenguia et al. / Intenational Jounal of Engineeing, Science and Technology, Vol., No. 1, 010, pp W c N V0 R C C a a Whee the paamete ( lsinφ d cos φ) = 8 πλμ '(1 ) (7) μ = R It is convenient to put Cx = Clcosφ+ Cd sinφ And Cy = Clsinφ Cd cosφ Solving Eqns. (3) and (7) to obtain values fo the flow induction factos a and a ' using two-dimensional aeofoil chaacteistics equies an iteative pocess. The following equations, deived fom Eqs. (3) and (7), ae convenient in which the ight-hand sides ae evaluated using existing values of the flow induction factos yielding simple equations fo the next iteation of the flow induction factos. a σ σ = C (8) x C y 1 a 4sin φ 4sin φ a ' σ Cy = (9) 1 + a ' 4sinφcosφ Blade solidity σ is defined as total blade aea divided by the oto disc aea and is a pimay paamete in detemining oto pefomance. Chod solidity σ is defined as the total blade chod length at a given adius divided by the cicumfeential length at that adius. Nc Nc σ = = (10) π πμr It is agued by Wilson and Lissaman (1974) that the dag coefficient should not be included in Eqs. (8) and (9) because the velocity deficit caused by dag is confined to the naow wake which flows fom the tailing edge of the aeofoil. Futhemoe, Wilson and Lissaman eason, the dag-based velocity deficit is only a featue of the wake and does not contibute to the velocity deficit upsteam of the oto disc. The basis of the agument fo excluding dag in the detemination of the flow induction factos is that, fo attached flow, dag is caused only by skin fiction and does not affect the pessue dop acoss the oto. Clealy, in stalled flow the dag is ovewhelmingly caused by pessue. In attached flow it has been shown by Young and Squie (1938) that the modification to the inviscid pessue distibution aound an aeofoil caused by the bounday laye has an affect both on lift and dag. The atio of pessue dag to total dag at zeo angle of attack is appoximately the same as the thickness to chod atio of the aeofoil and inceases as the angle of attack inceases. One last point about the BEM theoy: the theoy is stictly only applicable if the blades have unifom ciculation, i.e., if a is unifom. Fo non-unifom ciculation thee is a adial inteaction and exchange of momentum between flows though adjacent elemental annula ings. It cannot be stated that the only axial foce acting on the flow though a given annula ing is that due to the pessue dop acoss the disc. Howeve, in pactice, it appeas that the eo involved in elaxing the above constaint is small fo tip speed atios geate than 3. The complete pocedue can be witten as: (i) Guess a and a ' ( a = a ' = 0 is acceptable to stat Hau (006)); (ii) Calculate φ fom R 1 a tanφ = X 1 + a ' (iii) Calculate α fom α = φ β ; (iv) Calculate Cl and Cd fom gaph and table; (v) Calculate C and C fom x C = C cosφ+ C x l d C = C sinφ C y l d y sinφ cosφ

6 30 Tenguia et al. / Intenational Jounal of Engineeing, Science and Technology, Vol., No. 1, 010, pp (vi) Calculate a fom a σ σ = C x C y 1 a 4sin φ 4sin φ (vii) Calculate a' fom a ' σ Cy = 1 + a ' 4sinφcosφ (viii) Calculate Cp fom (ix) C = 4 a(1 a) p Go to step (ii) These equations ae solved iteatively because of the dependency between a, a', C, C, φ andσ. 4. Results and Discussion In this wok, the blade is divided into ten elements and all paametes such as chod, thickness, twist and powe coefficient ae calculated on these elements. 4.1 Chod and Thickness Distibution A chod diection is pependicula to the span diection and lies in the plane extending though the leading edge and the tailing edge. A shoulde is the point whee chod is maximum and it is minimum at the tip of the blade. Stesses ae maximum at the blade oot so that the blade oot is the thickest potion of the blade. The thickness distibution is calculated in tems of the chod whee the total thickness of the blade at any station will be a pecentage of the chod length at that station. Figue shows the chod distibution fo fou and five digit aifoils. Figue 3 and Figue 4 show the thickness distibution. Both chod and thickness ae educing fom oot to tip. The chod is calculated on the concept used by Ryu (004). x y Chod Distibution Figue : Chod distibution fo fou (NACA 441) and five digit (NACA ) aifoil

7 31 Tenguia et al. / Intenational Jounal of Engineeing, Science and Technology, Vol., No. 1, 010, pp Thickness Distibution Figue 3: Thickness distibution fo fou digit (NACA 441) aifoil Thickness Distibution Figue 4: Thickness distibution fo fou digit (NACA 441) aifoil 4. Twist Distibution The twist of a wind tubine blade is defined in tems of the chod line. It is a synonym fo the pitch angle. Howeve, the twist defines the pitch settings at each station along the blade accoding to the local flow conditions. The pitch angle (β) is lage nea the oot (whee local speeds ae low), and small at the tip (whee local speeds ae high). The appaent wind angle changes along the blade due to the incease in blade speed with inceasing distance outboad. Hence, to maintain optimum angle of attack of the blade section to the wind, it must be twisted along its length. In this wok, the twist distibution is maintained such that the lift

8 3 Tenguia et al. / Intenational Jounal of Engineeing, Science and Technology, Vol., No. 1, 010, pp coefficient will be maximum at evey station Hau (006). Figue 5 and Figue 6 give the twist distibution fo fou and five digit aifoils. The twist distibutions ae calculated fo diffeent tip speed atios Twist Distibution Figue 5: Twist distibution fo fou digit (NACA 441) aifoil Twist Distibution Figue 6: Twist distibution fo five (NACA ) digit aifoil

9 33 Tenguia et al. / Intenational Jounal of Engineeing, Science and Technology, Vol., No. 1, 010, pp Powe Coefficient In this pape, elemental powe coefficient is calculated at elements of the blade based on blade element momentum theoy. The lift coefficient is constant thoughout the blade fo both aifoils. The atio of C l /C d is fo fou digit aifoil and 71.9 fo five digit aifoil espectively. The Figue 7 and Figue 8 show the elemental powe coefficient fo fou and five digit aifoils espectively at fou diffeent tip speed atios based on blade element momentum theoy given in Hau, (006). 0.7 Elemental Powe Coefficient Figue 7: Elemental powe coefficient fo fou digit (NACA 441) aifoil 0.7 Elemental Powe Coefficient Figue 8: Elemental powe coefficient fo five digit (NACA ) aifoil

10 34 Tenguia et al. / Intenational Jounal of Engineeing, Science and Technology, Vol., No. 1, 010, pp Conclusion This pape pesents the investigation of blade pefomance fo a 5 KW hoizontal axis wind tubine based on blade element momentum theoy. The most difficult issues fo the BEM theoy ae: mathematical epesentation of the coect lift and dag coefficient values and coect evaluation of the axial and tangential induction factos. The blades having constant lift to dag atio coesponding to all elements ae investigated. Two NACA aifoils ae taken in this wok (the fou digit one and the five digit one). Fo the selected aifoils and the blade numbe, the chod, thickness and twist decease as we move fom oot to tip. At the blade oot, chod and thickness attain thei maximum values. Twist is maintained in such a manne that the angle of attack gives the maximum lift coefficient. Chod distibution is same fo both aifoils at all tip speed atios. Twist distibution is diffeent in both aifoils at diffeent tip speed atios. The value of elemental powe coefficient is maximum fo elements whee vaies fom 0.3 to 0.6. The natue of the flow patten aound an aeofoil is detemined by the Reynolds numbe and this significantly affects the values of the lift and dag coefficients. The powe coefficient of a oto vaies with the tip speed atio (the atio of oto tip speed to fee wind speed) and is only a maximum fo a unique tip speed atio. The maximum powe coefficient that can be achieved in the pesence of dag is significantly less than the Betz limit at all tip speed atios. Dag educes the powe coefficient at high tip speed atios. Stuctual and CFD analysis of the designed blade can also be done. Nomenclatue a a ' B c R W C C C C l d x y p Axial intefeence facto Rotational intefeence facto Numbe of blades Chod Radius of blade element o point on blade Blade tip adius Wind velocity elative to a point on otating blade Section lift coefficient Section dag coefficient Coefficient of sectional blade element foce nomal to the oto plane Coefficient of sectional blade element foce paallel to the oto plane C Powe coefficient ρ σ Ω λ α θ φ Refeences Ai density Roto solidity Rotational speed of oto Tip speed atio Blade segment angle of attack Angle of blade chod with oto plane Angle of elative wind fom oto plane Abbott I.H. and Vonoenhoff AET. In: Theoy of wing sections. Ince NY: Dove. Ackemann T. Sode,L. 00. An oveview of wind enegy-status 00. Renew. Sustain Enegy Rev., Vol. 6 pp Fuglsang P. L. and Madsen H. A. (1999). Optimization Method fo Wind Tubine Rotos. Jounal of Wind Engineeing and Industial Aeodynamics. Vol. 80. pp Fuglsang P. l. 00. Aeodynamic design guidelines fo wind tubine otos. In: CD-Rom poceedings, Vol. 4. GRACM congess on computational mechanics, Patas (GR), 7-9 J. T.sahalis, D.T. (ed.). Giguee, P and Selig M. S Blade Geomety Optimization fo the Design of Wind Tubine Rotos. 000 ASME Wind Enegy Symposium, Reno NV. Glauet H Duand WF edito. Aeodynamic theoy, Vol. IV, Division L. Aiplane popelles, chapte XI. Belin.. pp Giffiths R.T The effect of aifoil chaacteistics on windmill pefomance. Aeonautical Jounal. Vol. 81, No. 7, pp Habali S.M Designing and testing of small mixed aifoil wind tubine blades. J. Renewable Enegy, Vol Hassanein A, El-Banna H, Abdel-Rahman M Effectiveness of aifoil aeodynamic chaacteistics on wind tubine design pefomance. In: Poceeding of Seventh Intenational Confeence on Enegy and envionment, Vol. I, Caio, Egypt, Mach. pp

11 35 Tenguia et al. / Intenational Jounal of Engineeing, Science and Technology, Vol., No. 1, 010, pp Hau. E Wind tubines fundamental, technologies, application, economics. Kailling, Spinge. Johansen J., Madsen H.A., Gaunaa, M., Bak, C D Navie-Stokes Simulations of a oto designed fo Maximum Aeodynamic Efficiency 45. AIAA Aeospace Sciences Meeting and Exhibit, Reno. NV Lanzafame R., M. Messina 007. Fluid dynamics wind tubine design: Citical analysis, optimization and application of BEM theoy. J. Renewable Enegy. Vol. 3, pp Liu X., Yan C., Zhiquan. Y Optimization model fo oto blades of hoizontal axis wind tubine.font. Mech. Eng. China. Vol., No. 4, pp Lock C. N. H Expeiments to veify the independence of the elements of an aiscew blade. ARCR R&M No Maalawi K.Y, Badawy MTSA 001. Diect method fo evaluating pefomance of hoizontal axis wind tubines. Renewable and sustainable Enegy Review, Vol. 5, pp Madsen H.A., Mikkelsen R., Johansen J., Bak, C., Øye, S., Søensen, N.N Inboad oto/blade aeodynamics and its influence on blade design. In: Bak, C. (ed.), Reseach in Aeoelasticity EFP. Risø-R-1559(EN). Nagai B.M., Ameku K. and Roy J.N., 009. Pefomance of a 3 kw wind tubine geneato with vaiable pitch contol system, Applied Enegy, Vol. 86, No. 9, pp Nygaad T. A Optimization of wind tubine otos, doctoal thesis, Nowegian Univesity of Science and Technology. ISBN Ryu J.Y. and D. H. Kim. 004 Blade design of a 360 KW Diect dive wind tubine geneato system. Poceeding of ACCM4, Sydney. Snel, H Review of aeodynamics fo wind tubines. Wind Enegy, Vol. 6, pp Snel H Review of the pesent status of oto aeodynamics, Wind Enegy, Vol. 1, pp Spea D. A Wind Tubine Technology. New Yok: ASME Pess. Tangle J., 000.The evolution of oto and blade design, NREL/CP Pesented at the Ameican Wind Enegy Association Wind Powe, Palm Spings, Califonia, Apil 30.May 4 Wilson R. E. and Lissaman P. B. S. Applied aeodynamics of wind-powe machines. NTIS: PB , Oegon State Univesity, USA. Young, A. D. and Squie, H. B The Calculation of the Pofile Dag of Aeofoils R&M No Biogaphical notes Nitin Tenguia is a eseach schola in Depatment of Applied Mechanics in MANIT Bhopal India and he eceived his M.Tech. Fom MANIT Bhopal India D. N.D. Mittal is a Pofesso in Depatment of Applied Mechanics in MANIT Bhopal India. He has moe than 35 yeas of expeience in teaching and eseach. D. Siaj Ahmed is a Pofesso in Depatment of Applied Mechanics in MANIT Bhopal India. He has moe than 5 yeas of expeience in teaching and eseach. Received Septembe 010 Accepted Decembe 010 Final acceptance in evised fom Decembe 010