Rotor Design and Analysis of Stall-regulated Horizontal Axis Wind Turbine

Transcription

1 Roto Design and Analysis of Stall-egulated Hoizontal Axis Wind Tubine Xinzi Tang Univesity of Cental Lancashie, Peston, UK Xiongwei Liu Univesity of Cental Lancashie, Peston, UK Ahmad Sedaghat Univesity of Cental Lancashie, Peston, UK Lik-kwan Shak Univesity of Cental Lancashie, Peston, UK Abstact Wind enegy povides enegy secuity at a ti when deceasing global eseves of fossil fuel theatens the longtem sustainability of enegy supply. The powe pefomance of a wind tubine depends on the site s wind speed distibution and the design chaacteistics of the wind tubine. Based on the elationship between the powe pefomance and the oto paates, this pape addesses the design tip speed atio, ated wind speed, oto diate, and blade geoty of a stallegulated wind tubine. As a case study, a dedicated aeofoil is used fo the design and analysis of a stall-egulated wind tubine blade based on a specific wind speed distibution. Index Tems Blade elent montum theoy; Hoizontal axis wind tubine; Powe pefomance; Roto design; Stall-egulated; Site-specific wind tubine I. INTRODUCTION Renewable enegy is essential to the UK Govennt's objectives to educe cabon dioxide emissions by 6% by 5 and to geneate 5% of the UK s electicity supply fom enewable souces by. As one of the main souces of enewable enegy, wind enegy is unde developnt with an expectation of an additional 4GW enegy capacity fom onshoe wind in the UK []. A wind tubine system extacts kinetic enegy of the wind into chanical powe and convets it to electical powe. As powe in the wind passes two diffeent systems befoe it can be used, the output amount of powe available is mainly affected by the efficiency of the tubine oto and the efficiency of the chanical and electical systems. Roto design is a complex poblem and it is impossible to expect the maximum efficiency without an optimization pocess []. Based on the classical blade elent montum (BEM) theoy, tendous effots have been put on wind tubine design and optimization, most of which take maximum annual enegy poduction o minimum cost of enegy as objectives []. The BEM theoy has been widely applied as its compaable simplicity and veified having an acceptable accuacy befoe stall in many industial cases. And the thods deived fom the BEM theoy have been conveted into computational codes [4;5]. Poviding a set of basic specifications and constains, these thods ae able to select a easonable design ove a ange of options. As design paates ae given befoe the optimization pocedue begins, the elationship between the powe pefomance and the oto paates is not fully undestood. Since the powe pefomance of a wind tubine depends on the design chaacteistics but also the site specific wind esouce, the oto configuation should be caefully consideed accoding to the site s wind speed distibution. Fix-pitch vaiable-speed (FPVS) stall-egulated hoizontal axis wind tubines (HAWT) ae ecognized as a viable appoach of powe contolling in lieu of expensive pitchcontolled wind tubines. The oto speed can be contolled within a cetain ange accoding to the maximum powe coefficient law below ated wind speed. At above ated wind speed, the tubine limits its peak powe by well designed blade stall. The design pocedue and powe pefomance estimation of a thee-blade, upwind, stall-egulated HAWT is discussed in the following sections. The elationship between powe pefomance and oto specific paates is analyzed and pesented with a case study. II. ROTOR DESIGN METHODOLOGY In the design pocedue, the main paates such as aeofoil type, design tip speed atio, ated wind speed, oto diate, should be consideed fist befoe conducting blade geoty optimization. A. Aeofoil selection Aeofoil fo HAWT is often designed to be used at low attack angle, whee the dag coefficient is usually much lowe than the lift coefficient. A geneal aviation aeofoil shape is NACA seies, and dedicated aeofoil shapes used in moden wind tubines ae: S8 seies developed by National Renewable Enegy Laboatoy (NREL) in USA, FFA-W seies developed by FOI in Sweden, RisØ-A seies developed by RisØ in Denmak, DU seies developed by Delft Univesity of Technology in Nethelands. It has been found in so applications that moe than one aeofoil shape can be used fo the wind tubine blade design, but thee will be bending between these aeofoils which may add to uncetainties in the design pocess. Fo a stall-egulated wind tubine, it is bette to choose an aeofoil shape to make sue that stall occus gently afte the maximum lift-to-dag point. Design a wind tubine fo a specific site should not only include an optimum geoty with the maximum powe coefficient but also the detailed powe coefficient cuve which is a function of wind speeds o the tip speed atio. With moe accuate aeodynamic coefficients at high attack angles, the moe accuate design and pefomance pediction can be obtained. But the

2 aeodynamic coefficients of a otating aeofoil ae diffeent fom the ones of a linea moving aeofoil. The coefficients fom wind tunnel testing ae acceptably accuate in steady flow, but in stall conditions, these coefficients ae always lack of accuacy o thee is no coefficient asued at vey high attack angles at all. The low maximum lift coefficient, % thickness-to-chod atio NREL S89 aeofoil has been extensively used in HAWT, and the post-stall aeodynamic chaacteistics of S89 have been investigated and published. It is also used as a base case in this pape. The modified lift and dag coefficients fo steady-state and post-stall pefomance pediction ae shown in Fig.. These coefficients wee pesented with consideation of -dintional flow [6;7]. The lift coefficient fo the S89 aeofoil inceases to. at an attack angle of 5, but then it deceases as attack angle inceases. The dag coefficient inceases afte an attack angle of 9, and the maximum lift-to-dag atio occus at 8. As the wind speed inceases to high wind speed, the blade cos into deep stall egi; theefoe a constant powe can be achieved with a well-designed blade aeofoil. Lift Coefficient () and Dag Coefficient (Cd) Cd Attack Angle (degee) Fig.. Modified lift and dag coefficients of S89 aeofoil B. Design tip speed atio Given an aeofoil, the design tip speed atio is the fist paate that used in a blade design pocedue, which is geneally taken as 6-8 in moden wind tubines. But the optimum value emains uncetain fo diffeent aeofoil shapes and blade numbes[8;9]. It was claid that NACA 445 has an optimum tip speed atio of 8.5 while LS- has an optimum value of in -blade tubines[8]. As a highe lift coefficient s a lage lift foce, a highe dag coefficient s a lage dag foce, a tubine with the aeofoil of a highe lift coefficient and a lowe dag coefficient is expected to poduce moe powe with bette load conditions. The maximum lift-to-dag atio should be used in the optimal design, and the attack angle at which the maximum lift-to-dag atio occus should be consideed to be the optimal attack angle. This optimal attack angle, which is equal to the angle of elative wind minus twist angle and pitch angle at all sections when the blade geoty is optimal designed accoding to the BEM theoy, should be used in the design to calculate ideal powe coefficient. The BEM theoy divide a blade into seveal sections fom oot to tip and the total powe coefficient is calculated by integating the powe coefficients at these sections, as descibed in []: C p = (8 ) h F sin [ (Cd ) cot ϕ] d ϕ(cos ϕ sin ϕ)(sin ϕ + cos ϕ) Hee, Cp is the powe coefficient, is the lift coefficient, Cd is the dag coefficient, is the tip speed atio, h is the speed atio at hub (oot), is the local speed atio at position /R, φ is the angle of elative wind, and F is the tip loss facto. Fo a local loss calculation, it is descibed as Pandtl s loss facto [], which is a function of the local elative angle and the local tip speed atio. Hee, fo the oveall powe coefficient calculation of an ideal pe-designed blade, it can be efeed as follows, whee Z is the numbe of blades, Cpschmits is the theoetical coefficient including whilpool losses[9]:.84 Cp = Cpschmitz ( ) ( ) () Cd Z Fom the above equations, it can be seen that thee is a elationship between the ideal total powe coefficient and diffeent tip speed atios. Given a maximum lift-to-dag atio, the ideal total powe coefficients vesus diffeent tip speed atios can be obtained. Fom the modified lift and dag coefficients published, fo S89 aeofoil, a maximum lift-todag atio of 55.6 occus at an attack angle of 8, the ideal powe coefficients vesus diffeent tip speed atios ae plotted in Fig.. It is shown that the optimum tip speed atio fo S89 is aound 8. Powe Coefficient Tip Speed Ratio Fig.. Ideal powe coefficient cuve of an S89 aeofoil C. Rated wind speed The ated wind speed is the wind speed at which the wind tubine is geneating its ated powe. And the wind powe is popotional to the cube of the wind speed; high wind speed ()

3 s high powe can be poduced. Howeve, a highe ated wind speed is not always a good choice as the annual powe output is also a function of the local wind speed distibution, which is geneally descibed as Weibull distibution with a shape paate and a scale paate. The annual powe output can be calculated as: P annual = 876 ρac cut out cut in v Cp(v)f Weibull ( v) dv (MWH) () Whee,ρ=.5 kg/m is the ai destiny at the sea level, A, is the wind tubine oto aea, in m, C is the chanical and electical system efficiency, and Cp is the aeodynamic powe coefficient of the oto, which is basically detemined by the oto design and is a dinsionless function of wind speed (o tip speed atio). Fo a stall-egulated wind tubine, thee is not a simple way to expess the eal powe output exactly in a mathematical expession at above ated speed. But fo estimation, between the cut-in wind speed and the ated wind speed, the oto should wok at its maximum efficiency with an optimum contol stategy, and between the ated wind speed and the cut-out wind speed, the oto is expected to poduce a constant ated powe. And the Weibull paates vay with local wind conditions, the shape paate hee is taken as as an example hee. With a shape paate of Weibull distibution is also known as Rayleigh distibution, then () is conveted into: P annual + = 876 C 876 ρac P cut out ated ated speed atedspeed cut in π v v Cp(v) V π v V v exp π 4 V v exp π 4 V dv ( MWH ) (4) Based on the above analysis, it is obviously that choosing an appopiate ated wind speed based on the local wind distibution is citical fo the annual powe output. An impotant paate to descibe wind esouce used is annual wind speed. It seems that given a high wind speed V, it is possible to poduce moe powe with a high ated wind speed. With a low wind speed esouce, it is likely to poduce moe powe with a low ated wind speed. But it is shown in the following analysis that it is not the wind speed should be selected as ated wind speed. As the wind powe is popotional to the cube of the wind speed, let s define the annual cubic wind speed: V cubic = v f Weibull(v)dv (m/s) (5) and defining the annual wind speed as: V = vf Weibull(v)dv (m/s) (6) then we can establish the elationship between the annual cubic wind speed and the wind speed. By defining a dinsionless facto c: Vcubic C = (7) V dv With a shape paate of, the annual cubic wind speed is found about.4 tis as wind speed: C = v π v v exp( )dv π 4 v v V =.4 A Matlab pogam has been developed to find the elationship between the annual powe output and the ated wind speed based on the ideal powe output fom (4). It is found that an optimum ated wind speed depends on the wind speed. With Cp=.4, C =.8, ss shown in Fig., fo a kw wind tubine, with a wind speed highe than m/s, the annual powe output is lowe with a highe facto k, whee k is defined as k=vated / V. But it is also woth emphasizing that a lowe ated wind speed s a lage geneato, which causes an incease in cost. Annual Powe Output (MW) k= k=. k= Annual Mean Wind Speed (m/s) Fig.. Annual powe output vesus aveage wind speed of a kw tubine, k=vated / V D. Roto size Given a ated wind speed, V, in m/s, the powe extacted by the oto fom the wind, P, in W, is defined as: P = C p ρv πr (W) (9) Hee, R is the oto adius, in te, ρ =.5kg / m is the ai destiny (assuming at the sea level), Cp is the powe coefficient. Given the ated powe P and the pobable powe coefficient Cp, the oto adius can be estimated fom the above equation. Obviously, as the oto adius inceases, the powe output inceases. But it is not a good idea to expand the oto adius to incease the powe output as the expansion of the oto adius will esult in a highe cost. The powe output can be only impoved by a caeful aeodynamic design of the blade shape. E. Chod and twist distibution Detemination of the blade aeodynamic shape with the chod length distibution and twist distibution at a cetain design tip speed atio at which the blade has a maximum powe coefficient is the main task of the design fo blade with a known aeofoil. The geoty of the blade is an (8)

4 aeodynamic shape with nonlinea chod and twist distibution, which can be obtained based on the BEM theoy with espect to a cetain aeofoil type. It can be seen fom () that, thee is a elationship between these design paates and the maximum powe coefficient. If the main pat of the equation is at its maximum, as shown in (), the total powe coefficient is maximized. F sin ϕ(cos ϕ sin ϕ)(sin ϕ + cos ϕ) () [ (C d C l ) cot ϕ] Max Ignoing the dag-to-lift coefficient atio and setting the patial deivative of the main pat to zeo, the optimum design equation fo any kind of aeofoil can be obtained []: ϕ = tan () 8π C = ( cosϕ ) () Z The chod and twist distibutions fom the above equations ae just an initial design values and iteations ae followed nomally. So modifications of the twist angle and chod length distibutions may be conducted to decease the dag and thust foces to the oto at high winds. Howeve they should be close to the theoetical distibutions so as to make sue the maximum powe coefficient and low stat-up chaacteistics can be achieved. III. CASE STUDY A case study has been conducted with a kw fix-pitch vaiable-speed stall-egulated hoizontal axis wind tubine, and with the specifications of the oto listed in Table I. The local wind speed distibution is set to fit Rayleigh distibution with the UK wind speed of 5m/s at the oto cente height, and a ated wind speed of 8m/s is selected. The blade has an aeofoil of S89 with a thickness of % chod length along the blade except fo the tansitional egion fom the oot to the fist section of S89 aeofoil, and the design tip speed atio is set at 8. IV. RESULTS AND DISCUSSION The blade geoty is divided into sections, and the initial distibutions of the twist and the chod ae shown in Fig.4 and Fig.5. The Powe coefficients of all the sections ae plotted in Fig.6. The powe coefficients vesus oto otational speed with diffeent tip speed atio ae plotted in Fig.7. TABLE I ROTOR SPECIFICATIONS Rated powe w Rated wind speed m/s 8 Aeodynamic powe coefficient.4 Numbe of blades Design tip speed atio 8 Mechanical and electical efficiency.8 Radius of the oto m 5 Design attack angle degee 8 Fig.4 and Fig.5 demonstate that the chod length is lage at the inne sections of the blade (close to the oot) and smalle at the oute sections of the blade. The twists of the sections close to the oot ae lage than those close to the tip. The oot sections ae set to high twist angles, which contibute to the lowe stat up pefomance as the lage twist angle makes the oot sections to have an appopiate attack angle at a low stat-up wind but ae moe likely to stall at high wind speed. And the twist angle at the tip section is about.69 degee which also makes the tip sections moe likely to stall at high wind speeds but will contibute at low wind speed. Theefoe modifications should be balanced between the two aspects. Any modification should make the eal attack angle to appoximate the optimum attack angle and make sue the lift foce is not deceased shaply. Fig.6 eveals that the oute sections poduce most of the powe at the ated wind speed. Theefoe, any modification fo manufactuing consideations on the chod length and twist distibutions of these sections should be limited close to the initial optimal design to ensue ated powe. Chod (m) Twist (degee) Position (/R) Fig.4. Chod distibution of an initial blade design Position (/R) Fig.5. Twist distibution of an initial blade design

5 It is suggested in Fig.7 that, to obtain a maximum powe coefficient befoe the ated wind speed, the oto otational speed should be vaiable accoding to the maximum powe coefficient point. A detailed contol stategy can be implied, which is out of the the of in this pape. Powe Coefficient V. CONCLUSION Vaious oto paates wee investigated in this pape, and the oto design and analysis wee conducted based on a case of S89 aeofoil. The outco demonstates that: Powe Coefficient Position (/R) Fig.6. Powe coefficient distibution of an initial blade design wind speed = 5 m/s wind speed = 6 m/s wind speed = 7 m/s wind speed = 8 m/s 4) The ated wind speed should be selected based on the local site s wind speed. 5) The chod and twist distibution of the blade can be obtained based on BEM theoy, and any modifications on chod and twist distibutions should appoximate the optimum distibution. 6) A detailed powe coefficient cuve can be pedicted based on lift and dag coefficients consideing - dintional flow fo stall-egulated wind tubines. Accoding to the powe coefficient cuve, the maximum powe coefficient contol stategy can be applied. ACKNOWLEDGEMENTS The fist autho gatefully acknowledges the financial suppot of Univesity of Cental Lancashie Addison Studentship fo this study. REFERENCES [] R. AMA, "Wind Powe Constuction Pogam - UK 8-," Repot, 8 [] V. Ali and E. Bulent, "Pinciple of oto design fo hoizontal axis wind tubines," Jounal of Applied Sciences, vol. 6, no. 7, pp. 57-5, 6 [] E. Benini and A. Toffolo, "Optimal design of hoizontal-axis wind tubines using blade-elent theoy and evolutionay computation," Jounal of Sola Enegy Engineeing-Tansactions of the As, vol. 4, no. 4, pp. 57-6, [4] K. Y. Maalawi and M. A. Bad, "A pactical appoach fo selecting optimum wind otos," Renewable Enegy, vol. 8, no. 5, pp. 8-8, Ap. [5] M. e. Juan and G. David, "Wind blade chod and twist angle optimization by using genetic algoithms," Institute of Intelligent Systems and Nuical Applications in Engineeing.Univ.Las Palmas de Gan Canaia.5 Las Palmas,Spain., 9 [6] J. Tangle and J. David Kocuek, "Wind Tubine Post-Stall Aifoil Pefomance Chaacteistics Guidelines fo Blade-Elent Montum Methods," NREL/CP-5-69, Oct.4 [7] M. Kik, "Site Specific optimization of Roto/Geneato Sizing of Wind Tubines," Thesis,Geogia Institute of Technology, Dec.6 [8] N. S. Çetin, M. A. Yudusev, R. Ata, and A. Özdemi, "Assessnt of optimum tip speed atio of wind tubines," Mathematical and Computational Applications, vol., no., pp , 5 [9] M. A. Yuduseva, R. Atab, and N. S. Çetin, "Assessnt of optimum tip speed atio in wind tubines using atificial neual netwoks," Enegy, no., pp. 5-6, 6 [] J. Manwell, "Wind enegy explained: theoy, design and application," John Wiley & Sons Inc, pp. 8-8, Roto Rotational Speed (RPM) Fig.7. Powe coefficient vesus oto otational speed of an initial blade design ) A set of optimum design paates should be consideed to achieve the maximum annual powe output with a local wind speed distibution. ) Fo a stall-egulated wind tubine, it is appopiate to choose an aeofoil shape to make sue gentle stall occus afte the maximum lift-to-dag point. ) The design tip speed atio should be selected accoding to the aeodynamic chaacteistics of the aeofoil.