na

oria

Brake state modelNREL wind rotor

enls acodreli

theotion of] mod

This paper compares two different (the most accredited) brakestatemodels to evaluate the performance of a HAWT. The two brake design of a horizontal axis wind turbine. It has very fast compu-

tational times and provides great accuracy compared with experi-mental data. This code is based on Blade Element Momentum(BEM) theory, and can be implemented to design a wind rotor, and/or evaluate its performance.

BEM theory based numerical codes subdivide the wind turbinerotor into annuli of dr thickness, the ow of each sector beingindependent of adjacent circular sector ows [17,23]. Applying theequations of momentum and angular momentum conservation, for

Abbreviations: BEM, Blade Element Momentum; HAWT, horizontal axis windturbine; NREL, National Renewable Energy Laboratory; BSM, brake state model; 1-D, One-dimensional; 2-D, Two-dimensional.* Corresponding author.

Contents lists available at

Renewable

journal homepage: www.els

Renewable Energy 50 (2013) 415e420E-mail address: mmessina@diim.unict.it (M. Messina).Today, many researchers are developing numerical codes based onBEM theory [2e11]. Industry also utilizes these numerical codes todesign HAWT. These numerical codes are 1-D codes and producereliable results provided certain criticalities are resolved. Thesecriticalities regard the correct representation of lift and drag coef-cients at high values of angle of attack, the implementation ofa post-stall model (to take into account radial ow along theblades) and the implementation of a brake state model (to correctlydetermine axial and tangential induction factors) [12e17].

numerical code. Next, the two brake state models were compared,predicting the power curves for the NREL wind rotor [22]. Inscientic literature [29], experimental measurements are reportedfor this wind turbine rotor. Finally, a comparison between thesimulated and experimental power curves is performed.

2. BEM theory, post-stall model and brake state model

The numerical code, developed in [13] is a 1-D code for the1. Introduction

The numerical codes based on BEMthe design and performance evaluabased on Glauert propeller theory [10960-1481/$ e see front matter 2012 Elsevier Ltd.http://dx.doi.org/10.1016/j.renene.2012.06.062turbine blades (Himmelskamp Effect), and the brake state models by Buhl, combined with the calculationof Jonkmans tangential induction factor.In scientic literature, Shens brake state model is commonly implemented within 1-D numerical

codes, based on BEM theory. Subsequently, a comparison with Shens brake state models was carried out.With the numerical code presented in this work, the power for an NREL wind rotor was predicted. Withthe numerical simulation, it was possible to notice when these different brake state model furnish resultsclose to experimental data.

2012 Elsevier Ltd. All rights reserved.

ry are powerful tools forHAWT. BEM theory isied for wind turbines.

state models are Shens [18,19] and Buhls [20,21] (here Buhlsmodel is combined with Jonkmans equation to determine thetangential induction factor).

First, a numerical code based on BEM theory [13] was devel-oped, and a post-stall model [13,17] was implemented within theBEM theoryCentrifugal pumpingIn this research, the authors have produced a numerical code based on BEM theory in conjunction withan aerodynamic post-stall model, indispensable for taking into account radial ow along the windKeywords:model are implemented.Advanced brake state model and aerodywind turbines

R. Lanzafame, M. Messina*

Department of Mechanical and Industrial Engineering, University of Catania, Viale A. D

a r t i c l e i n f o

Article history:Received 20 December 2011Accepted 30 June 2012Available online 4 August 2012

a b s t r a c t

In scientic literature, whdifferent brake state modewhich is a 1-D numericalmance. This code providesAll rights reserved., 6, 95125 Catania, Italy

the aerodynamic design of a horizontal axis wind turbine is discussed,re presented. The brake state models are implemented within a BEM codee, based on Glauert propeller theory, and able to predict HAWT perfor-able results only if a proper brake state model and aerodynamic post-stallmic post-stall model for horizontal axis

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evier .com/locate/renene

The curve t can be applied to any airfoil in the same aero-dynamic region (the fully stalled one), because in this region thebenets due to radial ow are greater [33].

To increase CL distribution in the fully stalled region, a newapproach was implemented. As shown in Fig. 2, a fth-order log-arithmic polynomial CL

Pifcosti*lnaig was adopted for the

attached ow region (2 a 18), while for the dynamic stallregion (18 a 90) the function CL 2CLmax*sin(a)*cos(a) was

dR resultant force from lift and drag [N]dN normal rotor force [N]dT tangential rotor force [N]c airfoil chord [m]r air density [kg/m3]CL airfoil lift coefcient [e]CD airfoil drag coefcient [e]CLmax CL at a 45.Nb number of blades [e]F tip loss factor [e]CN normal force coefcient [e]lr local tip speed ratio [e]C torque [Nm]P mechanical power [W]

ewable Energy 50 (2013) 415e420each innitesimal dr sector of the blade, the axial force and torquecan be dened (Eqs. (1) and (2)).

The axial force on the blade element of width dr is:

dN r2V20 1 a2

sin2fNbCLcos f CD sin f c dr (1)

The torque on the blade element of width dr is:

dC r2V01 asin f

,u r 1 a0

cos fNb CLsin f CD cos f c rdr

(2)

Fig. 1 shows the axial and tangential forces (dN and dT) for anannulus of width dr.

From Eq. (2) wind rotor power can be evaluated, as reported inEq. (3).

P Z

u dT (3)

while the power coefcient is given by Eq. (4)

cp P12rAV30

(4)

2.1. Post-stall model

Knowing the lift and drag coefcients (CL and CD) is cruciallyimportant for assessing the forces and torques according to Eqs. (1)

Nomenclature

A rotor area [m2]Re Reynolds number [e]a angle of attack []f incoming ow direction angle []u angular velocity [s1]a axial induction factor [-]a0 tangential induction factor [e]r local blade radius [m]V0 wind velocity far upstream [m/s]V1 relative airfoil velocity [m/s]dL lift [N]dD drag [N]

R. Lanzafame, M. Messina / Ren416and (2).A problem which might cause numerical instability is linked to

the mathematical description of the airfoil lift coefcient. Theairfoils experimental data is 2-D and taken from wind tunnelmeasurements. Furthermore, due to rotation, the boundary layer issubjected to Coriolis and centrifugal forces which alter the 2-Dairfoil characteristics. This is especially pronounced in stall. It isthus often necessary to extrapolate existing airfoil data into deepstall and include the effect of rotation [24e28].

Owing to radial ow along the turbine blades, mathematicalequations describing lift coefcient have to overestimate experi-mental CL values within a precise range of the angle of attack.Centrifugal pumping is a phenomenon which describes radial airow along blades [29,30]. This ow slows the ow detaching fromthe airfoil, causing an increase in airfoil lift.

To take into account radial ow along a rotating blade inscientic literature, many authors modify the CL distribution[29,31,32].adopted. This last function intersects the logarithmic polynomialcurve at about 1/2e1/3 of its descendent part. This methodfurnishes the correct amount of increase in CL in the fully stalledregion, and permits the 1-D numerical code, to take into accountradial ow along the blades.

Analogously to lift coefcient, two different mathematicalfunctions have been implemented to describe the drag coefcient.A fth-order logarithmic polynomial CD

Pifcosti*lna ig

was adopted for the attached ow region (2 a 18), while forthe dynamic stall region (18 a 90) the function CD CDmax*sin2(a) was adopted. The cos ti, in the CD logarithmic polynomial,have been evaluated through the least squares method, startingfrom the CD experimental data [21]. Also the CDmax has been ob-tained from CD experimental data.Fig. 1. Forces acting on the airfoil.

the simulated and experimental data on the mechanical power for

tion

ewable Energy 50 (2013) 415e420 4172.2. Brake state model

A brake state model is a set of mathematical equations imple-mented within a 1-D numerical code, based on the Blade ElementMomentum theory, to design and evaluate the performance ofhorizontal axis wind turbines.

The brake state model implements different mathematicalexpressions to evaluate the tangential (a0) and axial (a) induction

Fig. 2. Graphic visualiza

R. Lanzafame, M. Messina / Renfactors. In the numerical code presented in this paper, Eqs. (5)e(7)were implemented [13].

The numerical stability of the mathematical code depends ontangential (a0) and axial (a) induction factors. Before selecting thesemathematical expressions, many simulations have been carriedout, implementing different mathematical expressions for thetangential and axial induction factors. In all the simulations theresults were not good as those presented in this paper (see Fig. 3),and in some cases, the numerical code does not converge to thesolution, but diverges to an innite loop of calculations.

In Eqs. (5) and (6) the two mathematical expressions imple-mented in this code for the evaluation of the axial induction factorare reported:

for a < 0.4:

a 14Fsin2f

cNb2pr

CLcosf CDsinf 1

(5)

while for a 0.4 [20]:

a 18F 20 3CN50 36F 12F3F 4

p36F 50 (6)

In Eq. (7) the mathematical expression implemented in thiscode for the evaluation of the tangential induction factor is re-ported [21]:a0 12

1 4

l2ra1 a

s 1

!(7)

where F is the Prandtl tip loss factor, as reported in [29,31].The proposed post-stall model, in conjunction with the brake

state model, has been validate through the comparison between

of the post-stall model.the NREL wind turbine (see Fig. 3). The results of the numericalcode proposed in this work (including the post-stall modeldescribed in Subsection 2.1, and the brake state model described inSubsection 2.2), are very close to experimental data.

3. Comparison between experimental and simulated data

The numerical code produced by the authors, is implemented topredict the power curve of the NREL wind rotor [22]. The radius of

0

2

4

6

8

10

12

14

0 5 10 15 20 25 30

Mech

an

ical P

ow

er [kW

]

Wind Speed [m/s]

NREL wind rotor

Experimental data Simulated data

Fig. 3. Experimental mechanical power for the NREL wind turbine.

Fig. 4. Buhls brake state model.

ewable Energy 50 (2013) 415e420the rotor is 5.03 m and rotates at 72 r/min. The blade section is theS809 airfoil. The experiments were carried out in the worldsbiggest wind tunnel at NASA Ames.

The rotor blades are twisted and tapered. Power control ispassive and occurs by deep stalling a section of the wind turbineblades. One method to maintain almost constant the wind turbinepower, while the wind speed varies, is that to design the blades sothat they work in the deep stall region, and power production islimited by these aerodynamic conditions (see Fig. 3, for the windspeed varying from 10 m/s to 20 m/s).

Experimental measurements of power as wind speed varieswere taken from scientic literature [29].

In Fig. 3 the comparison between the experimental and simu-lated data is shown. It is possible to notice how the 1-D numericalcode proposed in this work (with the post-stall model, and thebrake state model described in Subsections 2.1 and 2.2) furnishesreliable results.

4. Numerical simulation and comparison of brake statemodels

The combined JonkmaneBuhl [20,21] brake state model isimplemented within the numerical code developed by the authors(see Eqs. (5)e(7)), and is compared with Shens brake state model[18,19].

Shens brake state model is represented by Eqs. (8)e(14).For a 1/3

a 11 CN

p2F

(8)

while for a 1/3

a 2 Y1

4Y11 F Y21

q21 FY1

(9)

a0 11 aFY21 a 1

(10)

with

Y1 4Fsin2fsF1CN

(11)

Y2 4Fsinfcosf

sF1CT(12)

F1 2pcos1

exp

g NbR r

2rsinf

(13)

g exp 0:125Nblr 21 0:1 (14)Figs. (4) and (5) show the brake state models.In [34], Glauert reported the experimental results showing that

the trust coefcient equation CN 4a(1 a) is not valid if the axialinduction factor exceeds 0.4. Glauert [34] gave a correction fordetermining the axial induction factor, when a > 0.4, valid only forF 1. If the losses at the tip of the blade are taken into account(F < 1), the correction proposed by Buhl [20] must be consideredand implemented. Fig. 4 shows Buhls brake state model inconjunction with experimental data taken from [23].

This correction is needed to eliminate the numerical instabilitywhich occurs when the Glauert correction is implemented in

R. Lanzafame, M. Messina / Ren418conjunction with tip losses.In 2005, Shen et al. [18] proposed a new tip loss correctionmodel to predict physical behavior close to the tip. The local thrustcoefcient is replaced by a linear relation when the axial inductionvalue is greater than a critical value (a 1/3). Fig. 5 shows Shensbrake state model in conjunction with experimental data takenfrom [23].

Implementing the numerical code, the BEM computation iscarried out using 20 blade elements distributed uniformly along theblade. Comparative axial induction factors are rst computed. InFig. 6, the axial induction factor is plotted as a function of radius.

The axial induction values are almost identical for the inner partof the blade but diverge when approaching the tip. This value islower than the value obtained with the Glauert model (reportedalso in [18]), but greater than the value obtained with Shens brakestate model. A greater a value implies less predicted power.

Fig. 7 shows the predicted power curves for the NRELwind rotor.It shows the predicted power curve of the simplied Glauert model[18], the predicted power curve of Shens model [18], and theFig. 5. Shens brake state model.

0.8 This workGlauert [18]

ewa0.1

0.2

0.3

0.4

0.5

0.6

0.7

a [a

xia

l in

du

ctio

n fa

cto

r]0.9

1

Shen et al. [18]

R. Lanzafame, M. Messina / Renpredicted power curve obtained with the code developed in thiswork. All the predicted power curves are compared with experi-mental data.

Notice how in Fig. 7, the power predicted in this work is veryclose to the experimental data for wind speeds varying from 5 to20 m/s. For wind speeds greater than 20 m/s, Shens BSM predictsa better curve.

In future research, a new strategy to implement both the BSMspresented here, will be taken into account. Each BSM will beimplemented for different wind speed ranges to maximize thecorrelation between experimental and simulated data.

5. Conclusions

The authors produced a numerical code based on BEM theory inconjunction with an aerodynamic post-stall model, indispensablefor taking into account radial ow along the wind turbine blades,

workshop on scientic use of submarine cables and related technologies(SSC); 2011. p. 1e6. http://dx.doi.org/10.1109/UT.2011.5774146.

00.25 0.5 0.75 1

r/R

Fig. 6. Axial induction factor at wind speed 7 m/s.

0

2

4

6

8

10

12

14

16

18

0 5 10 15 20 25 30

Po

we

r [k

W]

Wind Speed [m/s]

Shen el al. [18]Experimental [22]Glauert Tip Correction [18]This work

Fig. 7. Predicted power curves.

978e1-4577-0164-1/2011 IEEE.

[10] Duan Wei, Zhao Feng. Loading analysis and strength calculation of windturbine blade based on blade element momentum theory and nite elementmethod. In: Power and energy engineering conference (APPEEC), 2010 Asia-Pacic; 2010. p. 1e4. http://dx.doi.org/10.1109/APPEEC.2010.5448929. 978-1-4244-4813-5/2010 IEEE.

[11] Tenguria Nitin, Mittal ND, Ahmed Siraj. Investigation of blade performance ofhorizontal axis wind turbine based on blade element momentum theory(BEMT) using NACA airfoils. International Journal of Engineering, Science andTechnology 2010;2(12):25e35.

[12] Lanzafame R, Messina M. Horizontal axis wind turbine working at maximumpower coefcient continuously. Renewable Energy 2010;35:301e6.

[13] Lanzafame R, Messina M. Fluid dynamics wind turbine design: critical anal-ysis, optimization and application of BEM theory. Elsevier Science. RenewableEnergy November 2007;32(14):2291e305. ISSN: 0960-1481.

[14] Lanzafame R, Messina M. Design and performance of a double-pitch windturbine with non-twisted blades. Elsevier Science. Renewable Energy May2009;34(5):1413e20. ISSN: 0960-1481.

[15] Lanzafame R, Messina M. Optimal wind turbine design to maximize energyproduction. Proceedings of IMechE, Part A: Journal of Power and Energy 2009;223(A2):93e101. http://dx.doi.org/10.1243/09576509JPE679.

[16] Lanzafame R, Messina M. Power curve control in micro wind turbine design.Energy February 2010;35(2):556e61. http://dx.doi.org/10.1016/j.energy.2009.10.025. Elsevier Science ISSN: 0360-5442.and the brake state models by Buhl combined with Jonkmanstangential induction factor.

This brake state model was compared with that of Shen et al. topredict the power curve for an NREL wind rotor for which experi-mental mechanical power measurements are reported in scienticliterature.

The comparison highlighted two different behaviors for the twobrake state models which in this work better predict the powercurves at low and middle wind speeds, whereas Shens worksbetter at high wind velocities.

The advantages of the developed method are those of a 1-Dnumerical code: very little computational weight, the possibilityto effect many simulations in a very little time, the possibility toevaluate different geometrical congurations of thewind turbine inorder to obtain high power coefcient, maximize the AnnualEnergy Production.

The disadvantage of this numerical code is its precision. Thesedisadvantages can be overcome with a nal 3-D CFD simulation.

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[20] Buhl Jr ML. A new empirical relationship between thrust coefcient andinduction factor for the turbulent windmill state. technical report NREL/TP-500-36834. National Renewable Energy Laboratory; August 2005.p. 1e7.

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[31] Corten GP. Flow separation on wind turbine blades. PhD. thesis, UtrechtUniversity; January 2001.

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R. Lanzafame, M. Messina / Renewable Energy 50 (2013) 415e420420

Advanced brake state model and aerodynamic post-stall model for horizontal axis wind turbines1. Introduction2. BEM theory, post-stall model and brake state model2.1. Post-stall model2.2. Brake state model

3. Comparison between experimental and simulated data4. Numerical simulation and comparison of brake state models5. ConclusionsReferences