Tenguria, Mittal and Ahmed. Journal of Urban and Environmental Engineering, v.5, n.1, p ISSN doi: /juee.2011.v5n1.

Transcription

1 15 J U E E Journal of Urban and Environmental Engineering v.5 n ISSN doi: 1090/juee.011.v5n1503 Journal of Urban and Environmental Engineering EVALUATION OF PERFORMANCE OF HORIZONTAL AXIS WIND TURBINE BLADES BASED ON OPTIMAL ROTOR THEORY Nitin Tenguria 1 N. D. Mittal 1 and Siraj Ahmed 1 Deartment of Alied Mechanics Deartment of Mechanical Engineering Maulana Azad National Institute of Technology Bhoal India Received 08 Aril 010; received in revised form 13 June 011; acceted 19 June 011 Abstract: Keywords: Wind energy is a very oular renewable energy resource. In order to increase the use of wind energy it is imortant to develo wind turbine rotor with high rotations rates and ower coefficient. In this aer a method for the determination of the aerodynamic erformance characteristics using NACA airfoils is given for three bladed horizontal axis wind turbine. Blade geometry is obtained from the best aroximation of the calculated theoretical otimum chord and twist distribution of the rotating blade. Otimal rotor theory is used which is simle enough and accurate enough for rotor design. In this work eight different airfoils are used to investigate the changes in erformance of the blade. Rotor diameter taken is 8 m which is the diameter of VESTAS V8-1.65MW. The airfoils taken are same from root to ti in every blade. The design lift coefficient taken is 1.1. A comuter rogram is generated to automate the comlete rocedure. Chord Twist Power coefficient Aerodynamic design otimal rotor. 011 Journal of Urban and Environmental Engineering (JUEE). All rights reserved. Corresonding Author: Nitin Tenguria. nitintenguria@yahoo.co.in Journal of Urban and Environmental Engineering (JUEE) v.5 n

2 16 INTRODUCTION The ower efficiency of wind energy systems has a high imact in the economic analysis of this kind of renewable energies. The efficiency in these systems deends on many subsystems: blades gearbox electric generator and control. Some factors involved in blade efficiency are the wind features like its robabilistic distribution the mechanical interaction of blade with the electric generator and the strategies dealing with itch and rotational seed control. It is a comlex roblem involving many factors relations and constraints. The increasing awareness of the general ublic to climate change and global warming has rovided oortunities for wind turbine alications in the UK. The UK claims 40% of the wind energy resources of Euroe. Euroe leads the world with 70.3% (3GW eak) of the total oerational wind ower caacity worldwide (Ackermann & Soder 00). As well as large wind turbines oerating in oen areas on- and off-shore more small-scale wind turbines are being installed and oerated by homeowners and small enterrises. One of the differences between large- and smallscale wind turbines is that small-scale wind turbines are generally located where the ower is required often within a built environment rather than where the wind is most favorable. In such location the wind is normally weak turbulent and unstable in terms of direction and seed because of the resence of buildings and other adjacent obstructions. To yield a reasonable ower outut from a small-scale wind turbine located in this turbulent environment and to justify such an installation economically the turbines have to imrove their energy cature articularly at low wind seeds and be resonsive to changes in wind direction. This means that small-scale turbines need to be secifically designed to work effectively in low and turbulent wind resource areas. Currently manufacturers of small wind turbines in the UK are not seen to make an attemt to accelerate low-seed airflow rior to reaching the turbines rotating blades. The aerodynamic and structural design of rotors for horizontal axis wind turbines (HAWTs) is a multidiscilinary task involving conflicting requirements on for examle maximum erformance minimum loads and minimum noise. The wind turbine oerates in very different conditions from normal variation in wind seed to extreme wind occurrences. Otimum efficiency is not obtainable in the entire wind seed range since ower regulation is needed to revent generator burnout at high wind seeds. Otimum efficiency is limited to a single-design wind seed for stall regulated HAWTs with fixed seed of rotation. The develoment of suitable otimization methods for geometric shae design of HAWT rotors is therefore a comlex task that involves off-design erformance and multile considerations on concet generator size regulation and loads. In Maalawi & Badawy (001) based on Glauert (1958) solution of an ideal wind mill along with an exact trigonometric function method analytical closed form equations are derived and given for reliminary determination of the chord and twist distribution and variation of angle of attack of the wind along the blade is then obtained directly from a unique equation for a known rotor size and refined blade geometry. Glauert (1958; 1959) originated the basic aerodynamic analysis concet of airscrew roellers and windmills. He alied first the momentum and energy relationshis for simle axial flow and then considered the effects of flow rotation after assing through the rotor as well as the secondary flows near the ti and hub regions. Wilson & Lissaman (1974) and Wilson et al. (1976) extended the Glauert s work and resented a ste by ste rocedure for calculating erformance characteristics of wind turbines. Analysis was based on a two-dimensional blade element stri theory and iterative solutions were obtained for the axial and rotational induction factors. Later on Wilson (1980) outlined a brief review of the aerodynamics of horizontal axis wind turbines. The erformance limits were resented and short note was given on the alicability of using the vortex-flow model. In Kishinami et al. (00) aerodynamic erformance characteristics of the HAWT were studied theoretically by combination analysis involving momentum energy and blade element theory by means of the stri element method and exerimentally by the use of a subscale model. Three tyes of blade were examined under conditions in which the free stream velocity is varied from to 4.5 m/s for the oen tye wind tunnel with an outlet duct diameter of 8m. The blade consists of a combination of taered rectangular NACA44 series. The aeronautical characteristics of the HAWT emloying the three different tyes of blades are discussed by reference of ower and torque coefficients C and C q and to the ti seed ratio derived from the exerimental and analytical results. The outut regulation by variable itch control/fixed itch stall control method is also discussed in this context. This aer focuses on the method for erformance analysis. The suggested aroaches can be divided into two stages namely; (a) Calculation of the blade geometry i.e. the chord and twist distributions and (b) Calculation of elemental ower coefficient on the basis of otimal rotor theory. In the first stage the equations given in Martin & Hansen (008) are used for getting the chord distribution and in the second stage comuter rogramme is develoed for getting the other arameter of blade based on Egglestone & Stoddard (1987). This work is comletely based on comuter rogram. For validation the results are comared with ower Journal of Urban and Environmental Engineering (JUEE) v.5 n

3 17 coefficient of VESTAS V8-1.65MW (VESTAS 011) which is exerimental. Otimal Rotors The Glauert annulus momentum equation rovides the essential relationshis for analyzing each blade segment using two dimensional airfoil data. What is needed in design however is guidance in this infinite arameter sace toward that rotor aerodynamics that will be best for one articular urose. Thus otimal rotor theory. Glauert resented a blade element analysis to find the ideal windmill based on neglecting the airfoil drag but including wake rotation or swirl (Glauert 1935). This aroach was extended by Stewart (1976) to include the effect of drag so that the Glauert analysis becomes a sub case of the Stewart analysis for the case of infinite lift/drag ratio. The Glauert analysis is simle enough and yet accurate enough to be very useful in reliminary rotor design. It can be used directly as a synthesis rocedure whereas almost all other aroaches are really analysis rocedures. The results of the Glauert or Stewart ideal wind mill theory is a referred value of the roduct cc l at each blade segment as a function of local seed ratio x. This yet leaves the choice of c or of c l the remaining arameter then fallowing the ideal value of the roduct cc l. Although this single-oint otimal is extremely useful for first-cut design it rovides no information as to the sensitivity of the erformance to off-design oeration. That is it is quite ossible to come u with a design that has a very high C at one design ti seed ratio X but falls off quite raidly to either side and so fails to garner the most ower over a whole wind sectrum of velocities. In addition to modifying the Glauert otimal blade element theory to account for drag Stewart (1976) ointed out that the design freedom in satisfying the otimal roduct cc l can be used to find a chord c that will be otimal at two different seed ratios. This aroach yields a design that is insensitive to erformance degradation for off design conditions. The equations used in Glauert ideal wind mill theory are same as the two dimensional airfoil theory excet that the drag coefficient c d is assumed zero. The effect of wake rotation is included. In a well designed rotor with a carefully shaed airfoil the lift/drag ratio is very high on the order of 100 or so so that the neglect of drag during first cut otimization is justified. Subsequent use of Stewart theory usually results in small corrections to these results. From Glauert momentum vortex theory tan a R cl cos cd sin (1 a) = σ φ+ φ 8r sin φ a σr c sin φ c cosφ = + φ φ l d (1 a ) 8r sin cos u V (1 a) (1 a) Ω r+ w Ω r(1 + a ) x(1 + a ) 0 φ= = = a λ(tan φ ε) = + φ (1 a ) sin () (3) (4) (5) If c d is assumed to be zero dividing Eq. (3) by Eq. () gives: a (1 a) a(1 + a ) = tan φ Combining this with Eq. (4) gives: (1 + a ) V 1 = 0 = a a(1 a) Ω r x (6) (7) At each radius right side of Eq. (7) is constant and therefore the left side must remain constant also while the ower is maximized if the quantity a (1 a) from Eq. (5) is maximized. Performing these oerations using Lagrange multiliers yields: (1 3 a) a = (4a 1) (8) In the windmill state a must be ositive for ositive outut torque. Thus for small x a aroaches 1/4 and a becomes large whereas for large x a aroaches 1/3 and a aroaches zero. Substituting a from Eq. (8) into Eq. (7) yields the required relationshi between a and the local seed ratio x as follows: x= (4a 1) (1 a) (1 3 a) (9) Miller et al. (1978) give a ower series in 1/x as an aroximation for the inverse relationshi: w Bc clsin φ cd cos φ = w+ωr 8πr sinφcosφ (1) a x 79x 59049x (10) Journal of Urban and Environmental Engineering (JUEE) v.5 n

4 18 The corresonding relative wind angle φ can be found from Eq. (6) as given by 1 tan φ = (1 a)(1 3 a) a (11) The otimum blade layout in terms of the roduct of chord c and lift coefficient c l can be found from Eq. (1) with c d = 0. σcx l σlcx l BΩ = = ( ccl ) = 8 4 8π V0 4a 1 (1 a)(1 3 a) 1 a (1) As mentioned reviously there is still some design freedom in that both c and c l may be varied while their roduct satisfies Eq. (1). Thus if chord c is held constant c l (and hence α and θ) will follow Eq. (1). Likewise if c l (and hence α) is held constant chord c must vary according to Eq. (1) and the twist angle θ has been secified as a function of r. Alternatively Stewart (1976) has shown that the freedom in satisfying the roduct relation cc l can be used to define a blade that is otimal over a wider range i.e. that is insensitive to off-design conditions. Miller et al. (1978) also integrate the C relation along the blade to give closed form and series solutions for C. Thus from Eqs (5) (8) and (9): dc 1 (4a 1)(1 a)(1 a) = da X (1 3 a) (13) which must be integrated from a = 1/4 at r = 0 to the value of a at the ti a T given by: (1 a ) T X = (4aT 1) (1 3 at ) (14) The integration can be done in closed form resulting in: C 8 (7X + 15) 53 = 1 ln (16) 7 9X 8 X For any ti seed ratio X the local seed ratio is x = X.The arameter a is determined from Eq. (10) and hence φ from Eq. (11) the roduct cc l from Eq. (1) and C from one of the Eqs (13) through (16). To obtain a single oint otimum including the effects of drag Stewart begins by driving local ower coefficient: C 1 ρ c ( l sin d cos ) WrΩB c φ c φ r P = = ρv0 A ρ V0 (π r) (17) which by using W² = V 0 ²(1 a) + r²ω²(1 + a )² and Eq. (4) to eliminate x² reduced to C = (1 a)²(1+cot²φ)axλ(sinφ εcosφ). Then eliminating λ and exanding 1/(cotφ + ε)) in Taylor s series of two terms there results: C = 4 xa(1 a)(tanφ ε)(1 + ε tan φ ) (18) The last term 1 + ε tanφ is quite small imroving the accuracy less than 1 ercent for ε = 1 and φ = 40 degree. Thus in most cases it may be neglected leaving: C = 4 xa(1 a)(tan φ ε) (19) Since the otimum value of a is found to be quite insensitive to changes in ε this imlies that C decreases monotonically as ε increases. By defining local Froude efficiency η F = (7/16) C we can relate the erformance of each blade element to the ideal value of unity. After eliminating a : C ln + 63z 4 z 4z 160 = 79 X z 14z 7z z 5 (15) tan xtan φ= 1 a 1 + φ ε cosφ+ε For small ε this is closely given by: (0) where z = 1 3a T. A series exansion valid for large tiseed ratio X is: xtan 1 sec φ = a φ (1) If the function F = a(1 a)(tanφ ε) is then maximized using df/dφ = 0 with the relation between a Journal of Urban and Environmental Engineering (JUEE) v.5 n

5 19 and φ given imlicitly by Eq. (0) there results a quadratic equation as follows: δ δφ {sin φ(cos φ xsin φ)(sin φ+ xcos φ )} = 0 (4) atan φ (1 a) εsec φ + (1 a) = + a (tan φ ε) () Solving this quadratic the otimal value of a including the effect of drag is given by where 1 = + φ + + a sec [ G ( G H )] εsecφ G = (tan φ ε) and tan φ H = (tan φ ε ) (3) Thus a single oint otimization of a rotor- blade element given φ and ε roceeds as follows: 1. Find a from Eq. (3) asin φ. Calculate φ from λ= (1 a)(cot φ+ε) 3. Find a from a(tan φ ε) a = [(1 a)(cot φ+ε) a(tan φ ε)] (1 a) 4. Then x = [(1 + a ) tan φ] 5. C = 4 xa(1 a)(tan φ ε)(1 εtan φ ) Aerodynamic Design The aerodynamic design of otimum rotor blades from a known airfoil tye means determining the geometric arameters such as chord length distribution and twist distribution along the blade length for a certain tiseed ratio at which the ower coefficient of the rotor is maximum. For this reason firstly the change of the ower coefficient of the rotor with resect to ti seed ratio should be figured out in order to determine the design ti seed ratio X corresonding to which the rotor has maximum ower coefficient. The blade design arameters will then be according to this design ti seed ratio. Examining the lots between relative wind angle and local ti seed ratio for a wide range of glide ratios gives us a unique relationshi when the maximum elemental ower coefficient is considered and this relationshi can be found to be nearly indeendent of glide ratio and ti loss factor. Therefore the general relationshi can be obtained between otimum relative wind angle and local ti seed ratio which will be alicable for any airfoil tye. Equation (4) reveals after some algebra (Hau 006): 1 1 φ= tan (7) 3 x Twist distribution can be easily determined from Eq. (5) and for getting the chord the relation given in Cha. 8 was used (Martin & Hansen 008). Airfoil roerties C = C cosφ+ C sinφ (6) n l d c 8πaxsin φ = (7) R (1 abc ) n X In this work eight airfoils are taken four of them are four digit airfoils and other four are five digit airfoils. Reference (Abott & Vonoenhoff 1958) is used for taking the roerties of airfoils. The selection of airfoil is very imortant oint in designing an efficient rotor (Griffiths 1977; Hassanein et al. 000). Griffiths (1977) showed that the outut ower is greatly affected by the airfoil lift-to-drag ratio while Hassanein et al. (000) recommended that the airfoil be selected according to its location along the blade to ensure its highest contribution to the overall erformance. The numbering system for NACA wing sections of the four-digit series is based on the section geometry. The first integer indicates the maximum value of the mean-line ordinate y c in er cent of the chord. The second integer indicates the distance from the leading edge to the location of the maximum camber in tenths of the chord. The last two integers indicate the section thickness in er cent of the chord. Thus the NACA 41 wing section has er cent camber at of the chord from the leading edge and is 1 er cent thick. The numbering system for wing sections of the NACA five-digit series is based on a combination of theoretical aerodynamic characteristics and geometric characteristics. The first integer indicates the amount of camber in terms of the relative magnitude of the design lift coefficient; the design lift coefficient in tenths is thus three-halves of the first integer. The second and third integers together indicate the distance from the leading edge to the location of the maximum camber; this distance in er cent of the chord is one-half the number reresented by these integers. The last two integers indicate the section thickness in er cent of Journal of Urban and Environmental Engineering (JUEE) v.5 n

6 0 the chord. The NACA 301 wing section thus has a design lift coefficient of 0.3 has its maximum camber at 15 er cent of the chord and has a thickness ratio of 1 er cent NACA 41 NACA 41 NACA 441 NACA 444 RESULT AND DISCUSSION Chord Distribution and Twist Distribution The aerodynamically otimum distribution of chord and twist of the rotor blades deends on the selection of a articular lift and drag coefficient. The lift and drag coefficient are taken from Abott & Vonoenhoff (1958). The rotor taken in this work has the same airfoil rofile at inboard mid-san and outboard stations of the blade. The chord and twist distribution for airfoils taken in this work are given by Figs 1 5 as we can see from Figs and 3 there is very slight difference in chord distribution in both four digit and five digit airfoils. The blades are twisted to otimize the angle of attack at every element of the blade the design lift coefficient taken in this work is 1.1 and the ti seed ratio is 7. Twist Fig. 3 Twist Distribution for Four Digit Airfoils. NACA NACA 63-1 NACA 301 NACA Twist NACA 41 NACA 41 NACA 441 NACA Chord Fig. 4 Twist Distribution for Five Digit Airfoils Fig. 1 Chord Distribution for Four Digit Airfoils. 7 6 NACA NACA63-1 NACA301 NACA Chord Fig. 5 NACA Fig. Chord Distribution for Five Digit Airfoils. Journal of Urban and Environmental Engineering (JUEE) v.5 n

7 1 The Ti Seed Ratio is of very imortant in the design of wind turbine blade. If the rotor of the wind turbine rotates very slowly maximum wind will ass as it is through the ga between the rotor blades. Alternatively if the rotor rotates quickly the blurring blades will aear like a solid wall to the wind. Therefore wind turbines are designed with otimal ti seed ratios to extract as much ower out of the wind as ossible. When a rotor blade asses through the air it leaves turbulence in its wake. If the next blade on the sinning rotor arrives at this oint while the air is still turbulent it will not be able to extract ower efficiently from the wind. However if the rotor san a little more slowly the air hitting each turbine blade would no longer be turbulent. Therefore the ti seed ratio is chosen so that the blades do not ass through turbulent air. For small local ti seed ratio axial interference factor aroaches 1/4 and rotational interference factor becomes large whereas for large local ti seed ratio axial interference factor aroaches 1/3 and rotational interference factor aroaches zero. Figures 5 1 gives the difference between the values of a and a with resect to local ti seed ratio for both four and five digit airfoils. a &a' Fig. 8 NACA441. Axial Intereference Factor Fig. 9 NACA Fig. 6 NACA Fig. 10 NACA Fig. 7 NACA Fig. 11 NACA 63. Journal of Urban and Environmental Engineering (JUEE) v.5 n

8 C Power Coefficient Fig.1 NACA Figures gives the elemental ower coefficient of wind turbine blade. For calculating the elemental ower coefficient the blade was divided into 0 elements. As it can be seen from the figures the erformance of NACA 444 and NACA 301 are better then other airfoils. Figure 15 is showing the ower coefficient of VESTAS V8-1.65MW. C NACA NACA63-1 NACA 301 NACA 301 Fig. 13 Power Coefficient for Five Digit Airfoils NACA 41 NACA 41 NACA 441 NACA Fig.15 Power Coefficient of VESTAS V8-1.65MW (VESTAS 011). CONCLUSION A methodology has been resented in this work for designing the wind turbine blade. The aroach uses the formulation base on Glauert annulus momentum equation. The selected design arameters include the chord and twist distribution tye of airfoil ti seed ratio. A comuter rogramme is develoed for automating the calculations. Two families of NACA airfoils are taken in this work i.e. four-digit series and five-digit series. For the selected airfoils and the blade number the chord and twist decreases as we go from root to ti. The variation of the twist and chord is almost same for all airfoils used in this work. The values of axial interference and rotational interference factor are almost same for all airfoils taken in this work with resect to the local ti seed ratio. The elemental ower coefficient calculated in this work deends on local ti seed ratio axial interference factor rotational interference factor angle of relative wind form rotor lane drag to lift ratio. As it can be seen from Figs the elemental ower coefficient of airfoils NACA 441 and NACA 301 are higher than other airfoils. With the hel of comarison between the Figs it is easy to understand that the ower coefficient in the resent work is more. Nomenclature C Fig. 14 Power Coefficient for Four Digit Airfoils. NACA 41 NACA 41 NACA 441 NACA 444 a =Axial interference factor a = Rotational interference factor B = Number of blades c = Chord C l = Section lift coefficient C d = Section drag coefficient r = Local blade radius A = Rotor swet area F = Prandtl loss factor w = Local tangential wind velocity at rotor lane Journal of Urban and Environmental Engineering (JUEE) v.5 n

9 3 u = Wind seed through rotor lane x = Local seed ratio X = Ti seed ratio V 0 = Free-stream wind velocity C = Power coefficient ε = Drag/lift ratio α = Blade segment angle of attack θ = Angle of blade chord with rotor lane φ = Angle of relative wind from rotor lane Ω = Rotor angular velocity References Abott I.H. & Vonoenhoff A.E.T. (1958) Theory of wing sections. Incc NY: Dover. Ackermann T. & Söder L. (00) An overview of wind energystatus 00. Renew. Sustain Energy Rev. 6(1) doi: /S (0) Egglestone D.M. & Stoddard F.S. (1987) Wind turbine engineering design.van NostrandReinhold. Glauert H. (1935) Airlane roellers. From Div. L Aerodynamic Theory ed. W.F. Durand. Berlin: Sringer Verlag Glauert H. (1959) The elements of airfoil theory and airscrew theory. London: Cambridge Univercity ress. Griffiths R.T. (1977) The effect of airfoil characteristics on windmill erformance. Aeronautical J. 81(7) Hassanein A. El-Banna H. & Abdel-Rahman M. (000) Effectiveness of airfoil aerodynamic characteristics on wind turbine design erformance. Proc. Seventh International Conference on Energy and Environment vol. I. Cairo Egyt March Hau E. (006) Wind turbines: Fundamental technologies alication economics. Krailling Sringer 006. Kishinami K. Taniguchib H. Suzukia J. Ibano H. Kazunoud T. & Turuhamie M. (00) theoretical and exerimental study on aeronautical characteristics of horizontal axis wind turbine. Proc. 5th International Symosium on C&E00 and the 4th International WES Conference Tokyo Maalawi K.Y. & Badawy M.T.S. (001) A direct method for evaluating erformance of horizontal axis wind turbines. Renew. Sustain Energy Rev. 5() doi: /S (00) Martin O. & Hansen L. (008) Aerodynamics of wind turbine. Second edition. Earthscan. Miller R.H. Dugundji J. & Martinez-Sanchez M. (1978) Wind energy conversion. MIT Aeroelastic and Structures Research Lab TR through TR DOE Contract No. C t1 distribution categoryuc-60. Stewart H.J. (1976) Dual otimum aerodynamic design for a conventional windmill. AIAA Journal 14(11) doi: / VESTAS Vestas Wind Systems A/S. (011) Available in: htt:// Wilson R.E. & Lissaman P.B.S. (1974) Alied aerodynamics and wind ower machines. PB Reort No. NSF-RA-N NTIS Sringfield Virginia. Wilson R.E. (1980) Wind turbine aerodynamics. J. Industrial aerodynamics 5(4) Wilson R.E. Lissaman P.B.S. & Walker S.N. (1976) Aerodynamic erformance of wind turbines. Reort No. NSF/RA-7608 NTIS Chaters I-III Oregon State Univercity. Journal of Urban and Environmental Engineering (JUEE) v.5 n