Wind Turbine Performance in Controlled Conditions: BEM Modeling

Research ArticleWind Turbine Performance in Controlled ConditionsBEM Modeling and Comparison with Experimental Results

David A Johnson Mingyao Gu and Brian Gaunt

Department of Mechanical and Mechatronics Engineering University of Waterloo Waterloo Canada N2L 3G1

Correspondence should be addressed to David A Johnson da3johnsuwaterlooca

Received 17 December 2015 Accepted 24 April 2016

Academic Editor Funazaki Ken-ichi

Copyright copy 2016 David A Johnson et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

Predictions of the performance of operating wind turbines are challenging for many reasons including the unsteadiness of the windand uncertainties in blade aerodynamic behaviour In the current study an extended blade element momentum (BEM) programwas developed to compute the rotor power of an existing 43m diameter turbine and compare predictions with reported controlledexperimental measurements Beginning with basic blade geometry and the iterative computation of aerodynamic properties themethod integrated the BEM analysis into the program workflow ensuring that the power production by a blade element agreedwith its lift and drag data at the same Reynolds number The parametric study using the extended BEM algorithm revealed theclose association of the power curve behaviour with the aerodynamic characteristics of the blade elements the discretization ofthe aerodynamic span and the dependence on Reynolds number when the blades were stalled Transition prediction also affectedoverall performance albeit to a lesser degree Finally to capture blade finite area effects the tip loss model was adjusted dependingon stall conditions The experimental power curve for the HAWT of the current study was closely matched by the extended BEMsimulation

1 Introduction

With wind energy becoming an important part of the energymix for many countries it is desirable to improve our under-standing of its potential power output Ideally the loading ona wind turbine at a specific wind speed and its correspondingpower production would be known prior to constructionand installation Knowledge of a turbinersquos power output andloading not only helps with the design of turbine compo-nents such as nacelle bearings or tower structure but alsobears financial implications when assessing the feasibility ofwind as alternative energy

The power output of a wind turbine is closely associatedwith the blade aerodynamics One commonly used approachto predict the power produced by a rotor given the blade air-foil aerodynamic properties is the blade element momentum(BEM) theory In the current study a MATLAB programherein referred to as ldquoextended BEMrdquo was developed tocompute the rotor power of a turbine Beginning with bladegeometry it integrated the BEM analysis into the program

workflow To examine its accuracy the model predictions ofthe blade performance were compared to the experimentalpower measurements collected on a custom-built three-bladed horizontal-axis wind turbine (HAWT) [1 2] Thetesting was completed at a wind generation facility capableof producing controlled wind speeds at the University ofWaterloo Due to the custom turbine and wind facility it waspossible to test the turbine performance over a wide rangeof wind speeds and rotational rates which formed a uniqueaspect of this study

While other data sets are available for testingwind turbineperformance models [3 4] it has been shown that modelpredictions still vary widelyTherefore the data on the exper-imental turbine used in this study and its test conditions willbe provided in hopes of allowing other researchers to verifytheir respective models

The paper is organized as follows The wind facility andturbine parameters will be briefly outlined followed by adetailed description of the extended BEM workflow and itsinput parameters A comparison of the model predictions

Hindawi Publishing CorporationInternational Journal of Rotating MachineryVolume 2016 Article ID 5460823 11 pageshttpdxdoiorg10115520165460823

2 International Journal of Rotating Machinery

with the collected experimental data will then be presentedand discussed

2 Experimental Equipment

21 Wind Facility The wind generation facility where allexperimentswere conductedwas an open-looped tunnel with6 identical fans located near its entrance The fans werearranged in a 2 by 3 array and drove the flow at adjustable flowrates Each fan generated a maximum air flow of 787m3s at4135 Pa The air flow was discharged into a 854m long by823m wide by 59m high plenum where it was conditionedbefore entering a 195m long and 154m wide test area thatwas 78m high at the sides and 13m high at the peak ofa pitched roof With the turbine installed in the test areathe maximum nominal wind speed attained during testingwas 111ms Further details regarding the geometry and flowanalysis of this facility can be found in [1 2 6]

22 Turbine The HAWT used for the current study had a43m diameter rotor The hub was located 31m above theground The shaft tilt and nacelle yaw angles were set tozero The blades were made from an existing blade mouldand design and assembled without upwind or downwind pre-coning During experimentation the turbine rotor plane waslocated 796m downstream of the test area inlet in the flowdirection Power production tests were conducted for a nom-inal wind speed range of 64ms to 111ms while the turbineshaft rotational rate varied from 40 rpm to 200 rpm Moredetails of the turbine in relation to testing can be found inwork by Gaunt and Johnson [1]

23 Blades In order to effectively model the performance ofthe wind turbine the geometry of the manufactured bladeswas determined including the chord twist and airfoil distri-butions

The aerodynamic span of the blade did not start until aradius ratio of approximately 23 where the cross-sectionalprofile transitioned from a chamfered rectangle to an airfoilFrom the root to the tip of the aerodynamic span the bladechord 119888 decreased linearly from 018m to 0046m

119888 = minus0174 times (

119903

119903119879

) + 0220 (m) (1)

with 119903 representing the radial positionmeasured with respectto the centre of rotation and 119903

119879the tip radius

The twist of the blade 120573 is herein defined as the anglebetween the local chord of a section of the blade and thetip chord Accordingly the tip twist angle is 0∘ by definitionMoreover the tip pitch angle 120579

119879 is herein defined as the

fixed angle between the tip chord and the plane of rotationTherefore the local pitch of the blade 120579 that is the anglebetween the local chord and the rotor plane (Figure 1) isthe sum of 120573 and 120579

119879 As per the foregoing definitions the tip

pitch angle of theHAWTblade used for the current study wasfound to be 3∘ The twist angle distribution instead of mono-tonically decreasing toward the tip was found to be irregularConsequently a look-up table was prepared given in Table 1

Table 1 Twist angle distribution of the manufactured turbineblades

Radius ratio Twist angle119903119903119879

120573 (deg)025 825031 588041 385051 209061 216071 332080 155090 056100 000

Chord line

FN

L D

FT

120601

120601

Ωr(1 + a998400)

120572

W

120579

Uinfin(1 minus a)

Blade rotation plane

Figure 1 Velocity and force triangles for an airfoil section of arotating wind turbine blade

which listed the blade twist angle at regular radial positionsalong the blade

The airfoil distribution was determined at three pointsalong the blade root midsection and tip of the aerodynamicspan that is 23 615 and 100 of 119903

119879 The measured

profiles for each blade section from root to tip smoothed bythe AFSMO program [7] and scaled with respect to the localchord length are shown in Figure 2 Smoothing of the profileswas critical for the XFOIL subroutines to converge (seeSection 32)Themeasured tip profile is plotted againstNACA4415 airfoil [8] to show the close approximation of the formerto the latter which will be elaborated on in the subsequentsectionsThemaximum thickness and camber and their loca-tions on the unit-length chord of the respective airfoils at theaforementioned three points along the blade are summarizedin Table 2

3 Methodology

Themathematical procedure for predicting the power perfor-mance used in the current study was based on the classicalBEM theory but extended it such that the input data to theBEM algorithm was computed from the blade geometry andincluded in the iterative procedure of BEM

International Journal of Rotating Machinery 3

0 01 02 03 04 05 06 07 08 09 1minus01

0

01

02

xc

yc

(a)

0 01 02 03 04 05 06 07 08 09 1minus01

0

01

02

xc

yc

(b)

0 01 02 03 04 05 06 07 08 09 1minus01

0

01

02

xc

yc

(c)

Figure 2 Measured blade airfoil coordinates (a) root (b) midsection (c) tip with NACA 4415 airfoil (dashed line)

Table 2 Maximum thickness and camber and their respectivelocations on the unit-length chord of each blade section at threeradial positions root midsection and tip of the aerodynamic span

Root Midsection TipMaximum thickness 0195 0217 0164at 119909 0225 0300 0325Maximum camber 00755 00406 00326at 119909 0600 0375 0400

31 Classical BEM Theory BEM estimates the aerodynamicforces on a turbine blade and from there estimates overallturbine loading and power production It can be employedfor many design and analysis purposes such as an estimationof the forces that blades could exert on a support structureDetails of the general method can be found in [9ndash11]

311 Assumptions A basic BEM implementation relies onseveral assumptions to simplify the problem to a suitable levelfor initial turbine analysis [9] The first assumption is thatthere is no flow along the blade in the spanwise directionAdjacent elements therefore have no effect on each otherimplying that the force on each element is based on the lift anddrag of a 2D airfoil given identical relative velocity and angleof attack While radial flow occurs particularly near the tipthe assumption was necessary in order to simplify the modelPrandtlrsquos tip loss model can be employed to compensate forthe error stemming from this simplification

Moreover it is assumed that the incoming wind speeddoes not vary based on the position of a blade in the rotationwhich effectively states that there is no yawed flow or windshear present Based on the wind facility design investigatedin a previous study [1] the wind shear assumption wasconsidered valid due to the wind speed control The yawedflow condition was satisfied by orienting the rotor plane to be

perpendicular to the upwind flow thereby producing zeroyaw

312 Procedure Overview The BEM algorithm begins bydividing the blade into a user-specified number of elementsFor every blade element the relative wind speed119882 and theangle of attack 120572 are then determined by way of an iterativeprocedure that incorporates local aerodynamic events intomomentum conservation over a control volume formedaround the blade element The parameters that indicate con-vergence of iterations are known as the axial and tangentialinduction factors (Figure 1) The axial induction factor 119886represents effectively the reduction in the incoming windspeed 119880

infin due to the momentum exchange between the

wind and the turbine The tangential induction factor 1198861015840 isintroduced to capture the increase in the tangential velocityΩ times 119903 due to the wake rotation For simplicity the initialvalues for 119886 and 1198861015840 are often set to zero

Once the iterative procedure converges the coefficientsof lift and drag 119862

119871and 119862

119863 can be determined from119882 and

120572 and subsequently the lift and drag forces 119871 and 119863 can becomputed In order to determine the power produced by therotor it is assumed that 119871 and 119863 obtained at the midpointbetween element stations act across the whole width of theelement which becomes increasingly valid as the number ofblade elements is increased Moreover the nonaerodynamicpart of the blade does not contribute to rotor power pro-duction 119871 and 119863 are in turn transformed into a second pairof orthogonal force components one tangential to the rotorplane 119865

119879 which contributes singularly to torque and the

other normal to the rotor plane 119865119873 which contributes

singularly to thrustThe force relations are shown in Figure 1Summation of 119865

119879times 119903 from every blade element yields the

shaft torque from which the power produced by one bladeis determined according to Eulerrsquos turbine equation with itsimplicit assumptions [10] and is multiplied by the number


(II) Solution initialization (III) Prestall lift and prestalldrag

(IV) Full-range lift and full-range drag

(V) BEM algorithm(I) Blade geometry

Spanwisedistribution of blade elements

Aerofoil coordinates at the center of every blade element

Turbineoperation conditions

XFOILPrestall lift and drag coefficients

Viterna or AERODASPrestall and poststall aerodynamic data

ClassicalBEM

Converged power coefficients

Turbine parameters

Re and Ma numbers for everyblade element corresponding to atip speed ratio

Initialguesses of induction

factors

Start

Windturbine aerofoilsections

End

Yes

No

Figure 3 Flowchart of the extended BEM procedure for calculating wind turbine performance

of blades to give the total power produced by the rotor Thetotal power scaled by the available power gives the powercoefficient 119862

119901

32 Extended BEM Procedure According to the classicalBEM theory the aerodynamic forces on the blades dependsolely on the lift and drag characteristics of the airfoil shape ofthe blade elements which poses challenges for implementa-tion from several perspectives First of all a modern turbineblade is often obtained by solid fitting through a series of well-established aerodynamic profiles leading to blended crosssectionswhose coefficients of lift and drag119862

119871and119862

119863 are not

readily available Consequently for ease of implementationthe 2D aerodynamic properties of well-established airfoilshapes that have been obtained experimentally at select Reare often used to represent the entire blade throughout theiterative procedure In addition 119862

119871and 119862

119863are functions of

Reynolds andMachnumbers Re andMaThedependence onRe is in particular prominent in the range between 10 times 104and 10 times 106 [12] to which range the HAWT used for thecurrent study belonged Re and Ma in turn depend on theturbine blade relative wind speed119882 Moreover119882 is a func-tion of axial and tangential induction factors 119886 and 1198861015840 whichare computed iteratively until a desired tolerance is reachedAs a result 119862

119871and 119862

119863input to the BEM algorithm should be

modified with every iteration in accordance with the changesin induction factors

The extended BEM algorithm addressed the aforemen-tioned limitations by nesting the classical BEM theory ina more comprehensive performance calculation procedurewhose workflow is shown in Figure 3 Each step was imple-mented in the MATLAB language because it provided han-dling of large data structures which arose from definition ofthe workflow components as separate class objects andallowed for integration of external routines such as XFOILdescribed below The MATLAB code was written so as to beapplicable to any test case or blade design

The extended BEM first introduced XFOIL [13] to calcu-late 119862

119871and 119862

119863up to just beyond maximum lift and drag

based on the local airfoil profile and Re and Ma XFOILhas proven suitable for the analysis of subcritical airfoilseven with significant laminar separation bubbles [14] Arepresentative amplification factor for transition prediction119873crit was unknown due to the lack of experimental flow datain the vicinity of the blades so 119873crit values ranging from 6to 10 were examinedThe input to XFOIL included the airfoilcoordinates at the centre of every blade element which wereinterpolated from the smoothed measured airfoil profiles atthe root midsection and tip of the aerodynamic span as wellas Re and Ma for every blade element corresponding to a setof 119886 1198861015840 and tip speed ratio 120582 that is Ω times 119903

119879119880infin

120572 range of a variable-speed fixed-pitch wind turbineextends deep into stall The prestall aerodynamic propertydata output by XFOIL would not be sufficient to provide


the lift and drag values required by the BEM solver so theywere extrapolated to an angle of attack range from minus20∘ to90∘ utilizing two separate poststall models Viterna [15] and

AERODAS [16] Both poststall models not only served thepurpose of extending the lift and drag coefficients into thepoststall region with acceptable accuracy but also consideredaspect ratio AR to account for the three-dimensional natureof flow over a turbine blade of finite length Calculation of theprestall119862

119871and prestall119862

119863byXFOIL and extension into post-

stall by Viterna or AERODAS were both iterated to take intoaccount the changes in 119886 and 1198861015840 fromone iteration to the next

The full range of airfoil data served as input to a standardBEM calculation procedure (see Section 312) adjusted forPrandtlrsquos tip losses with discretion which was integrated asa concluding step in the iterative procedure The procedurecomputed by iteration 119886 and iteration 1198861015840 for every parametriccombination based on a convergence criterion of 001 andfrom there output 119862

119901 which was used to indicate ldquoglobalrdquo

convergence of the extended BEM algorithm If 119862119901changed

more than the desired tolerance which was set to 01 in thecurrent study another iteration would be initiated beginningwith XFOIL recomputing the prestall aerodynamic propertydata with 119886 and 1198861015840 obtained from the preceding iterationThe tip loss correction is worth further remark Tangler andKocurek [17] in their guidelines for applying the Viternamodel to BEM analysis observed better power predictionswhen the finite AR effects were taken into account bysimultaneously adjusting the 2D airfoil data for finite ARwiththe poststall model and enabling the tip loss model Howeverit can be argued that using the tip loss model on airfoil dataalready adjusted for finite blade length would overly compen-sate for the effects of finite AR As a result in executing theextended BEM algorithm the tip loss model was turned off ifthe 2D airfoil data were corrected and turned on otherwise

Following the aboveworkflowaparametric studywas car-ried out to investigate the impact of specific input parameterson modeling power performance The four variables (shownin Table 3) used in the parametric study were the nominalwind velocity the transition amplification factor the poststallmodel and the finite AR correction (either the poststallmodel or Prandtlrsquos tip loss correction) In accordance with thewind facility testing the incomingwind speedwas fixedwhilethe turbine shaft rotational speed was varied to produce thedesired range of tip speed ratios The maximum achievable 120582in experimental testing was 8 where 119862

119901was a maximum To

allow the actual peak location to be identified the range of tipspeed ratios investigated with BEM modeling was increasedto include 120582 = 10

321 Prestall Lift and Prestall Drag In order to evaluate howXFOIL would perform in predicting prestall 119862

119871and prestall

119862119863as a part of the extended BEM workflow it was applied

to NACA 4415 series airfoil section NACA 4415 airfoil waschosen because it was closely approximated by the airfoilprofile at the blade tip (Figure 2) and therefore characterizedin part the aerodynamic behaviour of the turbine bladeWhile a number of experimental studies on NACA 4415airfoil are available in the literature for example [8 18] thewind tunnel data published by Ostowari and Naik [5] was

Table 3 Matrix of the parametric study carried out using theextended BEM algorithm

119880infin

73ms 111ms119873crit 6 7 8 9 10Poststall model Viterna AERODASFinite AR correction Poststall model Prandtlrsquos tip loss

selected for comparison with the XFOIL predictions becausethey provided test results for Re of 25times105 50times105 75times105and 10 times 106 the lowest of which was representative of theaverage Re on the HAWT rotor at the maximum nominalwind speed [1] Furthermore this data set spanned 120572 rangeof minus10∘ to 110∘ and included the effects of varying AR frominfinity to 6 However only 119862

119871and 119862

119863data extending just

beyond stall for a blade of infinite AR the same extent towhich the XFOIL code could be usefully employed weregathered for comparison with the XFOIL predictions TheXFOIL analyses were performed for 120572 ranging from minus14∘to 20∘ at Ma = 01 and Re = 25 times 105 50 times 105 and75 times 10

5 respectively119873crit = 7 was prescribed for transitionprediction The prestall 119862

119871and prestall 119862

119863output from

XFOIL in comparison to the experimental measurements areshown in Figure 4

In reference to Figure 4 a few observations can be madeabout the accuracy of XFOIL with respect to the wind tunneltesting First of all XFOIL consistently overpredicted 119862

119871by

an average of 02 units in 120572 region where the lift curve slopewas moderately constant and considerably underpredicted119862119871below 120572 = minus7∘ Furthermore as noted by [5] the

experimental data saw the maximum lift coefficient 119862119871max

decreasewith increasingRe contrary to the trend for a typical2D section [19] to which the XFOIL 119862

119871curves conformed

The experimental stall angle of attack 120572stall was near 18∘ over

the Re range of 25 times 105 to 75 times 105 whereas the XFOIL 120572stallat Re = 25 times 105 was at least 5∘ lower than the higher Recounterparts Since Re = 25 times 105 represented a typical Reexperienced by the HAWT rotor under test conditions theuse of XFOIL in calculating its power performance suggestedpossible errors in 120572stall would be borne downstream in theextended BEMworkflow On the other hand the Re effect onthe lift characteristic though noticeable only in and aroundstall demonstrated the necessity of computing the prestall liftand prestall drag for blade elements based on local Re

For drag the Re effect was more difficult to discernAlthough Ostowari and Naik [5] reported that they observeda rather pronounced effect of Re variation on the prestalldrag by means of a wake rake survey they did not provideadditional data to elaborate this point The XFOIL 119862

119863results

shown in Figure 4 demonstrate that close to the stall point119862119863decreased with increasing Re A more evident conclusion

concerning drag was that fairly large discrepancies existedbetween experimental and numerical 119862

119863values which were

a result of the method that drag was determined experimen-tally and with XFOIL While Ostowari and Naik used thewind tunnel force balance system to obtain the drag mea-surement 119862

119863output by XFOIL was the product of applying

the Squire-Young formula at downstream infinity [13] Over


minus1

minus05

0

05

1

15

2

CL

minus20 minus10 0 10 20

120572 (deg)

minus1

minus05

0

05

1

15

2

CL


120572 (deg)

minus1

minus05

0

05

1

15

2

CL


120572 (deg)

0

005

01

015

02

CD


120572 (deg)

0

005

01

015

02CD


120572 (deg)

0

005

01

015

02

CD


120572 (deg)

Re = 25 times 105 Re = 50 times 105 Re = 75 times 105

Figure 4 Coefficients of prestall lift and prestall drag as a function of angle of attack measured by Ostowari and Naik [5] (square marker)and predicted by XFOIL (solid line) for a NACA 4415 blade of infinite aspect ratio (AR) at Re = 25 times 105 50 times 105 and 75 times 105

the range of 120572 investigated XFOIL consistently output lower119862119863values

322 Poststall Lift and Poststall Drag The method firstproposed by Viterna and Janetzke [15] for predicting poststallaerodynamic characteristics requires as input a reference 120572typically 120572stall its corresponding 119862119871 and 119862119863 and the bladeAR to extrapolate prestall 119862


119863to 120572 = 90∘

The blade AR served the purpose of adjusting 2D airfoil datato model the aerodynamic behaviour of finite-length airfoilsFor an AR of infinity that is AR = infin the Viterna equationsare as follows assuming that119862

119863of an infinite-length blade at

120572 = 90∘ equals 119862

119863of an infinite-length flat plate normal to

the freestream (119862119863= 2)

119862119871= sin 2120572 + (119862

119871stallminus sin 2120572stall)

sin120572stallcos2120572stall

cos2120572sin120572

(2a)

119862119863= 2 sin2120572 + (119862

119863stallminus 2 sin2120572stall)

cos120572cos120572stall

(2b)

Tangler and Kocurek [17] provided additional guidelinesfor the Viterna method as a global poststall model and notedthat the accuracy of the Viterna equations depended on themagnitude of 119862

119871and 119862

119863associated with the reference 120572 and

on whether 119862119871119862119863at the reference 120572 agreed with flat plate

theory They also used a weighted AR that resulted from theblade radius divided by the local chord at 80 radius whichwas adopted in the current study

Table 4 AERODAS input parameters that need to be adjusted forfinite aspect ratio The prime notation means that the parametersare for an infinite aspect ratio airfoil without it they would be for afinite aspect ratio airfoil

11986011986211987111015840 Angle of attack at maximum prestall 119862

119871


119863

11986211987111015840 Maximum prestall 119862

119871


119863

11987811015840 Slope of linear segment of prestall lift curve

The AERODAS model [16] was developed empiricallyby determining the best fit to a large database of airfoilswith various combinations of AR Re 120572 and so forth Asidefrom the input parameters for the Viterna model it requiresas input the zero-lift 120572 its corresponding 119862

119863 the slope

of the linear segment for the prestall 119862119871curve and the

maximum prestall 119862119863 The AERODAS model allows for

correcting the infinite-length airfoil data for AR by adjusting5 of the 7 input parameters See Table 4 for the list of theseAERODAS input parameters In the case of AR = infinhowever the input parameters need not be adjusted that is1198601198621198711 = 1198601198621198711

1015840 1198601198621198631 = 11986011986211986311015840 1198621198711max = 1198621198711max10158401198621198631max = 1198621198631max1015840 and 1198781 = 11987811015840 Furthermore thetwo empirical functions of AR involved in calculating themaximum poststall 119862

119871and poststall 119862

119863 respectively are

reduced to 1198652 = 1 and 1198662 = 1


minus15 0 15 30 45 60minus1

minus05

0

05

1

15

2

0

05

1

15

2

CL

CD

AR = infin AR = 12 AR = 6

120572 (deg)

minus15 0 15 30 45 60120572 (deg)

0

05

1

15

2CD

minus15 0 15 30 45 60120572 (deg)

0

05

1

15

2

CD

minus15 0 15 30 45 60120572 (deg)

minus15 0 15 30 45 60minus1

minus05

0

05

1

15

2

CL

120572 (deg)minus15 0 15 30 45 60

minus1

minus05

0

05

1

15

2

CL

120572 (deg)

Figure 5 Coefficients of poststall lift and poststall drag as a function of angle of attack measured by Ostowari and Naik [5] (square marker)and predicted by AERODAS (solid line) and Viterna (dashed line) for NACA 4415 blades having aspect ratios (AR) of infinity 12 and 6 atRe = 25 times 105

Since the NACA 4415 data set [5] extended to 120572 = 110∘it was also used to assess how well the two poststall modelsViterna and AERODAS were able to predict 119862

119871and 119862

119863

beyond stall The prestall 119862119871and 119862

119863curves of the blade with

infinite AR at Re = 25 times 105 from the experimental data setin question were input to the Viterna and AERODASmodelswhich were implemented for 120572 ranging from stall to 60∘ andforAR = infin 12 and 6 respectivelyThe output by theViternaand AERODAS models which included the poststall 119862

119871and

119862119863data as well as the prestall 119862

119871and 119862

119863data adjusted as per

AR versus the experimental measurements at Re = 25 times 105is presented in Figure 5

As shown in Figure 5 the AERODAS model produced119862119871and 119862

119863that in general followed the experimental data

points more closely in the poststall regime than did theViterna output over the entire range of AR investigated Thelatter consistently underpredicted 119862

119863in the poststall regime

Moreover the AERODAS model was able to predict theoccurrence of secondary stall whereas the Viterna outputfailed to show any sign of the phenomenon The robustperformance of the AERODAS method was expected sinceone of the data sets used inAERODASmodeling [16] was thatby Ostowari and Naik [5] However one subtle advantage theViterna model had over the AERODASmodel as reflected inview of AR = 6 and 12 was that the former predicted the loca-tion of 119862

119871maxmore accurately than the latter which tended

to delay the occurrence of 119862119871max

to a higher 120572

4 Results and Discussion

41 General Discussion The primary BEM output of interestwas coefficient of power as a function of tip speed ratio (120582)Before presenting 119862

119901versus 120582 resulting from different input

parameters it is necessary to discuss the number of iterationsand the number of blade elements 119899 used by the extendedBEM algorithm to compute meaningful power coefficientsFor every parametric combination investigated the numberof iterations to achieve convergence varied loosely with 120582 Forlarger tip speed ratios a second iteration in general brought119862119901within 01 of 119862

119901output of the subsequent iteration

However for smaller tip speed ratios where the blade airfoilsections were stalled and the interpolation of aerodynamicproperties was based on the poststall lift and drag data 119862

119901

output displayed oscillatory behaviour due in part to the com-paratively small numerical values and in part to the sensitivityof the poststall drag models to slight changes in their inputparameters such as 120572stall Therefore a maximum percentageuncertainty of 5 was present in 119862

119901values computed for

small tip speed ratios As for an optimal number of bladeelements it was determined by comparing 119862

119901based on an

increasing number of blade elements The power curves with119899 = 6 10 and 14 elements are plotted in Figure 6 Six bladeelements led to overpredictions of119862

119901at larger tip speed ratios

whereas the results based on 10 and 14 blade elements nearlyoverlapped each other over the entire range of 120582 indicatingconvergence of results Hence the aerodynamic span of


Table 5MaximumandminimumRe seen by the aerodynamic spanof the blade at 120582 = 4 and 120582 = 10 with 119880

infin= 73ms and 119880

infin=

111ms Model input119873crit = 7 AERODAS tip loss model on

119880infin(ms) 120582 Minimum Re (times105) Maximum Re (times105)

73 4 104 14910 244 350

111 4 159 22710 371 532

3 4 5 6 7 8 9 100000

0075

0150

0225

0300

0375

0450

Cp

120582

Figure 6 119862119901versus 120582 for 119899 = 6 (solid line) 10 (dashed line) and 14

(crossmarker) blade elements Model input119880infin= 11ms119873crit = 7

AERODAS tip loss model on

the blade was divided into 10 elements for subsequent cal-culations that is 215 cm wide per element The discrepancybetween the power curves based on coarser and finer bladeelement distributions validated the necessity of using theaerodynamic properties of local blade sections Meanwhile itsuggested possible errors inmodeling the power performanceof the HAWT used for the current study which stemmedfrom linear interpolation of the blade section profiles fromthe smoothed measured airfoil profiles at the root midsec-tion and tip of the aerodynamic span

42 Effect of Reynolds Number It was evident from the powercurves obtained with a nominal wind speed of 73ms and111ms (Figure 7) that119862

119901was not only a function of120582 but also

strongly dependent on Re Table 5 illustrates how Reynoldsnumbers based on converged iterations of the extended BEMalgorithm varied with 119880

infin Regardless of the poststall model

choice or how the finite AR effect was captured as reflected inturning on or off the tip loss model 119880

infin= 111ms resulted

in larger 119862119901for 3 le 120582 le 5 than did 119880

infin= 73ms The

discrepancy was even more discernible in the case of AERO-DAS amounting to over 50 at 120582 = 4 The contributingfactor to the trend could be traced back to the effect of Re onthe prestall lift and drag coefficients namely 119862

119871maxof every

airfoil section increased with Re (see Section 321) leading tohigher lift in the poststall region through the poststallmodelsSince power production was proportional to lift larger 119862

119901

resulted Changes in the freestream velocity indeed impactthe coefficient of power at a given tip speed ratio a similartrend could be said of the raw experimental 119862

119901by observing

closely the scatter of data points for 3 le 120582 le 5 in Figure 8(owing to the limitation of the test rig the maximum 120582for which experimental 119862

119901could be obtained dropped with

increasing 119880infin

such that 120582 ranged from 08 to 45 for 119880infin=

111ms [1])

43 Effect of Transition Amplification Factor Although theparametric study was carried out with 119873crit set to 6 7 89 and 10 only 119862

119901curves obtained with 119873crit = 6 8 and

10 were included in Figure 9 to show with clarity the effectof transition amplification factor on prediction of powerproduction From 119873crit = 6 to 119873crit = 10 an increase in 119862

119901

by less than 2 on average was present between 120582 = 5 and120582 = 9 Consequently from the perspective of modeling119873critcould be any number between 7 and 10 By investigating theaerodynamic data corresponding to the respective transitionamplification factors the reason for the increase in 119862

119901was

illuminated While 119873crit = 6 and 119873crit = 10 resultedin virtually the same prestall drag curve the latter yieldedhigher lift toward stall thereby giving rise to increased liftimmediately before and after the stall point which in viewof power production translated into the region of 119862

119901curve

preceding and following the peak 119862119901value According to the

review by van Ingen [20] which associated119873crit ranging from94 to 99 with a overall RMS turbulence level of 12 to 20 ofthe free stream speed119873crit = 10 could well represent the flowscenario simulated in the current study since the turbulenceintensity in testing was found to vary from 102 to 149depending on the freestream velocity [1] However as notedby various researchers [20 21] the freestream turbulence levelis not the only factor influencing transition Therefore thechoice of a representative 119873crit was convenient for modelingbut did not necessarily encompass all the physics of transitionencountered by the turbine blades

44 Comparison of Experimental and Extended BEM119862119901 The

impact on 119862119901of the remaining two input parameters of the

parametric study namely the poststall model and how theeffect of finite AR of the blade was captured is presented inconjunction with the experimental power curve in Figures 10and 11 Note that the experimental power curve resulted fromcurve fitting to scattered raw experimental119862

119901data (Figure 8)

and was found to contain a percentage uncertainty of approx-imately 7 [1] Because 119862

119901data obtained experimentally for

119880infin= 111ms only extended to 120582 = 45 the curve fit was

a closer representation of 119862119901data obtained experimentally

for 119880infin= 73ms Therefore the ensuing discussion on

comparison of experimental and extended BEM 119862119901will be

in reference to Figure 10The tip speed ratio representing the peak of a 119862

119901curve is

herein referred to as 120582peak AERODAS and Viterna predicted120582peak = 8 and 120582peak = 85 respectively as a result of theformer tending to delay the occurrence of 119862

119871maxto a higher

120572 (see Section 322) 120582peak for the experimental 119862119901curve

appeared to be 8 although the same pointmarked the last datapoint Since the experimental 119862

119901data did not reach a peak


3 4 5 6 7 8 9 100000

0075

0150

0225

0300

0375

0450

Cp

120582

(a)

3 4 5 6 7 8 9 100000

0075

0150

0225

0300

0375

0450

Cp

120582

(b)

3 4 5 6 7 8 9 100000

0075

0150

0225

0300

0375

0450

Cp

120582

(c)

3 4 5 6 7 8 9 100000

0075

0150

0225

0300

0375

0450

Cp

120582

(d)

Figure 7 119862119901versus 120582 for 119880

infin= 111ms (solid line) and 119880

infin= 73ms (dashed line) Model input (a)119873crit = 7 AERODAS tip loss model

on (b)119873crit = 7 AERODAS tip loss model off (c)119873crit = 7 Viterna tip loss model on (d)119873crit = 7 Viterna tip loss model off

and subsequently decrease the actual 120582peak was potentiallygreater than 8 in light of which Viterna was therefore themore favorable model Moreover with every other inputparameter held invariant AERODAS consistently yieldedsmaller power coefficients than did Viterna irrespective ofwhether or not the tip loss model was turned on The dis-crepancies only increased toward the lower and upper limitsof 120582 range investigated At lower tip speed ratios Viternaperformed better inmatching the experimental119862

119901curveThe

reason why 119862119901curves computed using Viterna and AERO-

DAS still differed for 120582 ge 120582peak when neither model wasused to correct for finite AR that is when the aerodynamicloads on the blade depended on the prestall lift and prestalldrag was that AERODAS interpreted prestall 119862

119871as having a

constant slope region [16] though that was not always acharacteristic of the XFOIL 119862

119871curves for the Re range

investigatedAs for the effect of turning on and off the tip loss model

the impact is made clear by both Figures 10 and 11 Regardlessof the choice of the poststall model correcting for the effectof finite AR through either AERODAS or Viterna and in

turn disabling the tip loss model saw 119862119901drop markedly

for 120582 ge 5 in reference to 119862119901obtained with the tip loss

model enabled The decrease in 119862119901made physical sense

Modeling the aerodynamic properties of every turbine bladesection on the lift and drag of a finite-length airfoil impliedthat nowhere along the blade did 2D flow dominate whichwas uncharacteristic of the blade particularly before stalland consequently led to more significant deviation from theexperimental 119862

119901curve in the corresponding 120582 range On the

other hand for 120582 le 55 it was observed from the Viternacurves in Figure 10 that adjusting the 2D airfoil data for finiteARbrought themodeled119862

119901results closer to their experimen-

tal counterparts suggesting the need for capturing in somedegree the cross-element flow interactions despite the inher-ent assumptions of classical BEM theory Hence a reasonablerule of thumb was to turn on the tip loss model prior tostalling of a good portion of the aerodynamic span of theblade and turn off the tip loss model after it

To summarize the foregoing observations the experi-mental power curve was best predicted by the extended BEMsimulation that used the Viterna method for producing the


0 1 2 3 4 5 6 7 8000

005

010

015

020

025

030

035

040

045

111ms104ms92ms

84ms73ms64ms

120582

Cp

Figure 8 Raw experimental 119862119901versus 120582 results for a 119880

infinrange of

64ms to 111ms [1]

3 4 5 6 7 8 9 100000

0075

0150

0225

0300

0375

0450

Cp

120582

Figure 9 119862119901versus 120582 for 119873crit = 6 (blue) 8 (red) and 10 (black)

Model input 119880infin= 111ms Viterna tip loss model on

poststall aerodynamic data corrected for the finite AR effectwith the poststall model after stall and with the tip lossmodel before it 119862

119901peak was accurately modeledThe largest

difference between the experimental and extended BEM 119862119901

curves which was 66 occurred at 120582 = 8 and was within thepercentage uncertainty of the experimental data

5 Conclusions

By incorporating the computation of aerodynamic propertiesinto its iterative procedure the extended BEM algorithmensured that the chord Reynolds number seen by a bladeelement was based on the converged axial and tangentialinduction factors and that the power production by the bladeelement agreedwith its lift anddrag data at the sameReynolds

3 4 5 6 7 8 9 100000

0075

0150

0225

0300

0375

0450

Cp

120582

Figure 10119862119901versus 120582 obtained experimentally (solid line) andwith

the extended BEM algorithm for119880infin= 73msModel input119873crit =

7 AERODAS (black) or Viterna (red) tip loss model on (dashedline) or off (cross marker)

3 4 5 6 7 8 9 100000

0075

0150

0225

0300

0375

0450

Cp

120582

Figure 11119862119901versus 120582 obtained experimentally (solid line) and with

the extended BEM algorithm for 119880infin= 111ms Model input

119873crit = 7 AERODAS (black) or Viterna (red) tip loss model on(dashed line) or off (cross marker)

number Convergence or slight oscillation of119862119901was generally

obtained after a few iterationsThe experimental power curvefor theHAWTof the current studywas closelymatched by theextended BEM simulation

The parametric study using the extended BEM algorithmrevealed in essence the close association of the power curvebehaviour with the aerodynamic characteristics of the bladeelements For a turbine blade with variable cross sections itwas important to discretize the aerodynamic span into anadequate number of blade elements A guideline based onthe HAWT of the current study was that each blade elementshould be at least 02m wide for a 43m diameter rotor Thedependence of turbine power output on Reynolds number inthe range of 10times104 to 10times106 was strong particularly when


the blades were stalled supported by both experimental andmodeling results Transition prediction also affected overallpower performance albeit to a lesser degree 119862

119901gradually

increased with larger transition amplification factors in theregion of the peak 119862

119901value Finally in order to more

accurately capture the finite AR effect of the blade the tip lossmodel should be selectively turned on or off the former beingpreferable when the blades were not stalled or close to stall

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

The authors would like to acknowledge the support ofthe Natural Sciences and Engineering Research Council ofCanada and the Ontario Centres of Excellence

References

[1] B Gaunt and D A Johnson ldquoWind turbine performance incontrolled conditions experimental resultsrdquo International Jour-nal of Green Energy 2012

[2] D Johnson A Abdelrahman and D Gertz ldquoExperimentalindirect determination of wind turbine performance and BladeElement Theory parameters in controlled conditionsrdquo WindEngineering vol 36 no 6 pp 717ndash738 2012

[3] M M Hand D A Simms L J Fingersh et al ldquoUnsteady aero-dynamics experiment phase VI wind tunnel test configurationsand available data campaignsrdquo Tech Rep NRELTP-500-29955NREL 2001

[4] J G Schepers and H Snel ldquoModel experiments in controlledconditions final reportrdquo Tech Rep ECN-E-07-042 ECN 2007

[5] COstowari andDNaik ldquoPost stall studies of untwisted varyingaspect ratio blades with an NACA 4415 airfoil sectionmdashpart IrdquoWind Engineering vol 8 no 3 pp 176ndash194 1984

[6] B Gaunt Power generation and blade flow measurements ofa full scale wind turbine [MS thesis] University of WaterlooWaterloo Canada 2009

[7] H L Morgan ldquoAFSMOAFSCL-airfoil smoothing and scalingrdquoNASA LAR-13132 NASA Washington Wash USA 1994

[8] I H Abbot and A E von Doenhoff Theory of Wing SectionsDover New York NY USA 1959

[9] T Burton D Sharpe N Jenkins and E BossanyiWind EnergyHandbook John Wiley amp Sons 2006

[10] M Hansen Aerodynamics of Wind Turbines Earthscan Ster-ling Va USA 2008

[11] JManwell JMcGowan andA RogersWindEnergy ExplainedJohn Wiley amp Sons 2009

[12] P B S Lissaman ldquoLow-Reynolds-number airfoilsrdquo AnnualReview of Fluid Mechanics vol 15 pp 223ndash239 1983

[13] M Drela and H Youngren ldquoXFOIL an analysis and designsystem for low Reynolds number airfoilsrdquo in Low ReynoldsNumber Aerodynamics Proceedings of the Conference NotreDame Indiana USA 5ndash7 June 1989 vol 54 of Lecture Notes inEngineering pp 1ndash12 Springer Berlin Germany 1989

[14] M S Selig A Gopalarathnam P Giguere and C A LyonldquoSystematic airfoil design studies at low Reynolds numbersrdquo inFixed Flapping and Rotary Wind Vehicles at Very Low Reynolds

Numbers pp 143ndash167 American Institute of Aeronautics andAstronautics 2001

[15] L Viterna and D Janetzke ldquoTheoretical and experimentalpower from large horizontal axis wind turbinesrdquo Tech RepNASA TM-82944 NASA 1982

[16] D A Spera ldquoModels of lift and drag coefficients of stalled andunstalled airfoils in wind turbines andwind tunnelsrdquo Tech RepNASACR-2008-215434 NASA Cleveland Ohio USA 2008

[17] J Tangler and JDKocurek ldquoWind turbine post-stall airfoil per-formance characteristics guidelines for blade-element momen-tum methodsrdquo Tech Rep NRELEL-500-36900 NationalRenewable Energy Laboratory Golden Colo USA 2004

[18] M J Hoffmann R Ramsay and G Gregorek ldquoEffects of gritroughness and pitch oscillations on the NACA 4415 airfoilrdquoNRELTP 442-7815 1996

[19] J Anderson Aircraft Performance and Design McGraw-HillInc 1999

[20] J L van Ingen ldquoThe e-to-the-N method for transition predic-tion Historical review of work at TU delftrdquo in Proceedings of the38th Fluid Dynamics Conference and Exhibit American Instituteof Aeronautics and Astronautics Seattle Wash USA 2008

[21] T Cebeci Stability and Transition Theory and ApplicationHorizons 2004

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



with the collected experimental data will then be presentedand discussed

2 Experimental Equipment

21 Wind Facility The wind generation facility where allexperimentswere conductedwas an open-looped tunnel with6 identical fans located near its entrance The fans werearranged in a 2 by 3 array and drove the flow at adjustable flowrates Each fan generated a maximum air flow of 787m3s at4135 Pa The air flow was discharged into a 854m long by823m wide by 59m high plenum where it was conditionedbefore entering a 195m long and 154m wide test area thatwas 78m high at the sides and 13m high at the peak ofa pitched roof With the turbine installed in the test areathe maximum nominal wind speed attained during testingwas 111ms Further details regarding the geometry and flowanalysis of this facility can be found in [1 2 6]

22 Turbine The HAWT used for the current study had a43m diameter rotor The hub was located 31m above theground The shaft tilt and nacelle yaw angles were set tozero The blades were made from an existing blade mouldand design and assembled without upwind or downwind pre-coning During experimentation the turbine rotor plane waslocated 796m downstream of the test area inlet in the flowdirection Power production tests were conducted for a nom-inal wind speed range of 64ms to 111ms while the turbineshaft rotational rate varied from 40 rpm to 200 rpm Moredetails of the turbine in relation to testing can be found inwork by Gaunt and Johnson [1]

23 Blades In order to effectively model the performance ofthe wind turbine the geometry of the manufactured bladeswas determined including the chord twist and airfoil distri-butions

The aerodynamic span of the blade did not start until aradius ratio of approximately 23 where the cross-sectionalprofile transitioned from a chamfered rectangle to an airfoilFrom the root to the tip of the aerodynamic span the bladechord 119888 decreased linearly from 018m to 0046m

119888 = minus0174 times (

119903

119903119879

) + 0220 (m) (1)

with 119903 representing the radial positionmeasured with respectto the centre of rotation and 119903

119879the tip radius

The twist of the blade 120573 is herein defined as the anglebetween the local chord of a section of the blade and thetip chord Accordingly the tip twist angle is 0∘ by definitionMoreover the tip pitch angle 120579

119879 is herein defined as the

fixed angle between the tip chord and the plane of rotationTherefore the local pitch of the blade 120579 that is the anglebetween the local chord and the rotor plane (Figure 1) isthe sum of 120573 and 120579

119879 As per the foregoing definitions the tip

pitch angle of theHAWTblade used for the current study wasfound to be 3∘ The twist angle distribution instead of mono-tonically decreasing toward the tip was found to be irregularConsequently a look-up table was prepared given in Table 1

Table 1 Twist angle distribution of the manufactured turbineblades

Radius ratio Twist angle119903119903119879

120573 (deg)025 825031 588041 385051 209061 216071 332080 155090 056100 000

Chord line

FN

L D

FT

120601

120601

Ωr(1 + a998400)

120572

W

120579

Uinfin(1 minus a)

Blade rotation plane

Figure 1 Velocity and force triangles for an airfoil section of arotating wind turbine blade

which listed the blade twist angle at regular radial positionsalong the blade

The airfoil distribution was determined at three pointsalong the blade root midsection and tip of the aerodynamicspan that is 23 615 and 100 of 119903

119879 The measured

profiles for each blade section from root to tip smoothed bythe AFSMO program [7] and scaled with respect to the localchord length are shown in Figure 2 Smoothing of the profileswas critical for the XFOIL subroutines to converge (seeSection 32)Themeasured tip profile is plotted againstNACA4415 airfoil [8] to show the close approximation of the formerto the latter which will be elaborated on in the subsequentsectionsThemaximum thickness and camber and their loca-tions on the unit-length chord of the respective airfoils at theaforementioned three points along the blade are summarizedin Table 2

3 Methodology

Themathematical procedure for predicting the power perfor-mance used in the current study was based on the classicalBEM theory but extended it such that the input data to theBEM algorithm was computed from the blade geometry andincluded in the iterative procedure of BEM


0 01 02 03 04 05 06 07 08 09 1minus01

0

01

02

xc

yc

(a)

0 01 02 03 04 05 06 07 08 09 1minus01

0

01

02

xc

yc

(b)

0 01 02 03 04 05 06 07 08 09 1minus01

0

01

02

xc

yc

(c)












119871and 119862

















ClassicalBEM


Turbine parameters



factors

Start


End

Yes

No



119901


119871and119862

119863 are not


119871and 119862



119871and 119862





119871and 119862



119879119880infin
















119871and prestall




119880infin



119871and 119862





119863output from



119871by








119863results








minus1

minus05

0

05

1

15

2

CL


120572 (deg)

minus1

minus05

0

05

1

15

2

CL


120572 (deg)

minus1

minus05

0

05

1

15

2

CL


120572 (deg)

0

005

01

015

02

CD


120572 (deg)

0

005

01

015

02CD


120572 (deg)

0

005

01

015

02

CD


120572 (deg)






119863to 120572 = 90∘



120572 = 90∘ equals 119862



119862119871= sin 2120572 + (119862



cos2120572sin120572

(2a)

119862119863= 2 sin2120572 + (119862



(2b)


119871and 119862






119871


119863


119871


119863



119863 the slope







reduced to 1198652 = 1 and 1198662 = 1


minus15 0 15 30 45 60minus1

minus05

0

05

1

15

2

0

05

1

15

2

CL

CD


120572 (deg)

minus15 0 15 30 45 60120572 (deg)

0

05

1

15

2CD

minus15 0 15 30 45 60120572 (deg)

0

05

1

15

2

CD

minus15 0 15 30 45 60120572 (deg)

minus15 0 15 30 45 60minus1

minus05

0

05

1

15

2

CL

120572 (deg)minus15 0 15 30 45 60

minus1

minus05

0

05

1

15

2

CL

120572 (deg)



119871and 119862

119863




119871and


119871and 119862










to a higher 120572







119901




119901based on an







infin=



73 4 104 14910 244 350

111 4 159 22710 371 532

3 4 5 6 7 8 9 100000

0075

0150

0225

0300

0375

0450

Cp

120582












infin= 73ms The


119871maxof every


119901


119901by observing





111ms [1])




119901


119901was


119901curve














119901curve is







3 4 5 6 7 8 9 100000

0075

0150

0225

0300

0375

0450

Cp

120582

(a)

3 4 5 6 7 8 9 100000

0075

0150

0225

0300

0375

0450

Cp

120582

(b)

3 4 5 6 7 8 9 100000

0075

0150

0225

0300

0375

0450

Cp

120582

(c)

3 4 5 6 7 8 9 100000

0075

0150

0225

0300

0375

0450

Cp

120582

(d)






119901curveThe



119871as having a















0 1 2 3 4 5 6 7 8000

005

010

015

020

025

030

035

040

045

111ms104ms92ms

84ms73ms64ms

120582

Cp


infinrange of

64ms to 111ms [1]

3 4 5 6 7 8 9 100000

0075

0150

0225

0300

0375

0450

Cp

120582







5 Conclusions


3 4 5 6 7 8 9 100000

0075

0150

0225

0300

0375

0450

Cp

120582




3 4 5 6 7 8 9 100000

0075

0150

0225

0300

0375

0450

Cp

120582









119901gradually




Competing Interests


Acknowledgments


References

























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 01 02 03 04 05 06 07 08 09 1minus01

0

01

02

xc

yc

(a)

0 01 02 03 04 05 06 07 08 09 1minus01

0

01

02

xc

yc

(b)

0 01 02 03 04 05 06 07 08 09 1minus01

0

01

02

xc

yc

(c)












119871and 119862

















ClassicalBEM


Turbine parameters



factors

Start


End

Yes

No



119901


119871and119862

119863 are not


119871and 119862



119871and 119862





119871and 119862



119879119880infin
















119871and prestall




119880infin



119871and 119862





119863output from



119871by








119863results








minus1

minus05

0

05

1

15

2

CL


120572 (deg)

minus1

minus05

0

05

1

15

2

CL


120572 (deg)

minus1

minus05

0

05

1

15

2

CL


120572 (deg)

0

005

01

015

02

CD


120572 (deg)

0

005

01

015

02CD


120572 (deg)

0

005

01

015

02

CD


120572 (deg)






119863to 120572 = 90∘



120572 = 90∘ equals 119862



119862119871= sin 2120572 + (119862



cos2120572sin120572

(2a)

119862119863= 2 sin2120572 + (119862



(2b)


119871and 119862






119871


119863


119871


119863



119863 the slope







reduced to 1198652 = 1 and 1198662 = 1


minus15 0 15 30 45 60minus1

minus05

0

05

1

15

2

0

05

1

15

2

CL

CD


120572 (deg)

minus15 0 15 30 45 60120572 (deg)

0

05

1

15

2CD

minus15 0 15 30 45 60120572 (deg)

0

05

1

15

2

CD

minus15 0 15 30 45 60120572 (deg)

minus15 0 15 30 45 60minus1

minus05

0

05

1

15

2

CL

120572 (deg)minus15 0 15 30 45 60

minus1

minus05

0

05

1

15

2

CL

120572 (deg)



119871and 119862

119863




119871and


119871and 119862










to a higher 120572







119901




119901based on an







infin=



73 4 104 14910 244 350

111 4 159 22710 371 532

3 4 5 6 7 8 9 100000

0075

0150

0225

0300

0375

0450

Cp

120582












infin= 73ms The


119871maxof every


119901


119901by observing





111ms [1])




119901


119901was


119901curve














119901curve is







3 4 5 6 7 8 9 100000

0075

0150

0225

0300

0375

0450

Cp

120582

(a)

3 4 5 6 7 8 9 100000

0075

0150

0225

0300

0375

0450

Cp

120582

(b)

3 4 5 6 7 8 9 100000

0075

0150

0225

0300

0375

0450

Cp

120582

(c)

3 4 5 6 7 8 9 100000

0075

0150

0225

0300

0375

0450

Cp

120582

(d)






119901curveThe



119871as having a















0 1 2 3 4 5 6 7 8000

005

010

015

020

025

030

035

040

045

111ms104ms92ms

84ms73ms64ms

120582

Cp


infinrange of

64ms to 111ms [1]

3 4 5 6 7 8 9 100000

0075

0150

0225

0300

0375

0450

Cp

120582







5 Conclusions


3 4 5 6 7 8 9 100000

0075

0150

0225

0300

0375

0450

Cp

120582




3 4 5 6 7 8 9 100000

0075

0150

0225

0300

0375

0450

Cp

120582









119901gradually




Competing Interests


Acknowledgments


References

























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation


















ClassicalBEM


Turbine parameters



factors

Start


End

Yes

No



119901


119871and119862

119863 are not


119871and 119862



119871and 119862





119871and 119862



119879119880infin
















119871and prestall




119880infin



119871and 119862





119863output from



119871by








119863results








minus1

minus05

0

05

1

15

2

CL


120572 (deg)

minus1

minus05

0

05

1

15

2

CL


120572 (deg)

minus1

minus05

0

05

1

15

2

CL


120572 (deg)

0

005

01

015

02

CD


120572 (deg)

0

005

01

015

02CD


120572 (deg)

0

005

01

015

02

CD


120572 (deg)






119863to 120572 = 90∘



120572 = 90∘ equals 119862



119862119871= sin 2120572 + (119862



cos2120572sin120572

(2a)

119862119863= 2 sin2120572 + (119862



(2b)


119871and 119862






119871


119863


119871


119863



119863 the slope







reduced to 1198652 = 1 and 1198662 = 1


minus15 0 15 30 45 60minus1

minus05

0

05

1

15

2

0

05

1

15

2

CL

CD


120572 (deg)

minus15 0 15 30 45 60120572 (deg)

0

05

1

15

2CD

minus15 0 15 30 45 60120572 (deg)

0

05

1

15

2

CD

minus15 0 15 30 45 60120572 (deg)

minus15 0 15 30 45 60minus1

minus05

0

05

1

15

2

CL

120572 (deg)minus15 0 15 30 45 60

minus1

minus05

0

05

1

15

2

CL

120572 (deg)



119871and 119862

119863




119871and


119871and 119862










to a higher 120572







119901




119901based on an







infin=



73 4 104 14910 244 350

111 4 159 22710 371 532

3 4 5 6 7 8 9 100000

0075

0150

0225

0300

0375

0450

Cp

120582












infin= 73ms The


119871maxof every


119901


119901by observing





111ms [1])




119901


119901was


119901curve














119901curve is







3 4 5 6 7 8 9 100000

0075

0150

0225

0300

0375

0450

Cp

120582

(a)

3 4 5 6 7 8 9 100000

0075

0150

0225

0300

0375

0450

Cp

120582

(b)

3 4 5 6 7 8 9 100000

0075

0150

0225

0300

0375

0450

Cp

120582

(c)

3 4 5 6 7 8 9 100000

0075

0150

0225

0300

0375

0450

Cp

120582

(d)






119901curveThe



119871as having a















0 1 2 3 4 5 6 7 8000

005

010

015

020

025

030

035

040

045

111ms104ms92ms

84ms73ms64ms

120582

Cp


infinrange of

64ms to 111ms [1]

3 4 5 6 7 8 9 100000

0075

0150

0225

0300

0375

0450

Cp

120582







5 Conclusions


3 4 5 6 7 8 9 100000

0075

0150

0225

0300

0375

0450

Cp

120582




3 4 5 6 7 8 9 100000

0075

0150

0225

0300

0375

0450

Cp

120582









119901gradually




Competing Interests


Acknowledgments


References

























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation























119871and prestall




119880infin



119871and 119862





119863output from



119871by








119863results








minus1

minus05

0

05

1

15

2

CL


120572 (deg)

minus1

minus05

0

05

1

15

2

CL


120572 (deg)

minus1

minus05

0

05

1

15

2

CL


120572 (deg)

0

005

01

015

02

CD


120572 (deg)

0

005

01

015

02CD


120572 (deg)

0

005

01

015

02

CD


120572 (deg)






119863to 120572 = 90∘



120572 = 90∘ equals 119862



119862119871= sin 2120572 + (119862



cos2120572sin120572

(2a)

119862119863= 2 sin2120572 + (119862



(2b)


119871and 119862






119871


119863


119871


119863



119863 the slope







reduced to 1198652 = 1 and 1198662 = 1


minus15 0 15 30 45 60minus1

minus05

0

05

1

15

2

0

05

1

15

2

CL

CD


120572 (deg)

minus15 0 15 30 45 60120572 (deg)

0

05

1

15

2CD

minus15 0 15 30 45 60120572 (deg)

0

05

1

15

2

CD

minus15 0 15 30 45 60120572 (deg)

minus15 0 15 30 45 60minus1

minus05

0

05

1

15

2

CL

120572 (deg)minus15 0 15 30 45 60

minus1

minus05

0

05

1

15

2

CL

120572 (deg)



119871and 119862

119863




119871and


119871and 119862










to a higher 120572







119901




119901based on an







infin=



73 4 104 14910 244 350

111 4 159 22710 371 532

3 4 5 6 7 8 9 100000

0075

0150

0225

0300

0375

0450

Cp

120582












infin= 73ms The


119871maxof every


119901


119901by observing





111ms [1])




119901


119901was


119901curve














119901curve is







3 4 5 6 7 8 9 100000

0075

0150

0225

0300

0375

0450

Cp

120582

(a)

3 4 5 6 7 8 9 100000

0075

0150

0225

0300

0375

0450

Cp

120582

(b)

3 4 5 6 7 8 9 100000

0075

0150

0225

0300

0375

0450

Cp

120582

(c)

3 4 5 6 7 8 9 100000

0075

0150

0225

0300

0375

0450

Cp

120582

(d)






119901curveThe



119871as having a















0 1 2 3 4 5 6 7 8000

005

010

015

020

025

030

035

040

045

111ms104ms92ms

84ms73ms64ms

120582

Cp


infinrange of

64ms to 111ms [1]

3 4 5 6 7 8 9 100000

0075

0150

0225

0300

0375

0450

Cp

120582







5 Conclusions


3 4 5 6 7 8 9 100000

0075

0150

0225

0300

0375

0450

Cp

120582




3 4 5 6 7 8 9 100000

0075

0150

0225

0300

0375

0450

Cp

120582









119901gradually




Competing Interests


Acknowledgments


References

























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










minus1

minus05

0

05

1

15

2

CL


120572 (deg)

minus1

minus05

0

05

1

15

2

CL


120572 (deg)

minus1

minus05

0

05

1

15

2

CL


120572 (deg)

0

005

01

015

02

CD


120572 (deg)

0

005

01

015

02CD


120572 (deg)

0

005

01

015

02

CD


120572 (deg)






119863to 120572 = 90∘



120572 = 90∘ equals 119862



119862119871= sin 2120572 + (119862



cos2120572sin120572

(2a)

119862119863= 2 sin2120572 + (119862



(2b)


119871and 119862






119871


119863


119871


119863



119863 the slope







reduced to 1198652 = 1 and 1198662 = 1


minus15 0 15 30 45 60minus1

minus05

0

05

1

15

2

0

05

1

15

2

CL

CD


120572 (deg)

minus15 0 15 30 45 60120572 (deg)

0

05

1

15

2CD

minus15 0 15 30 45 60120572 (deg)

0

05

1

15

2

CD

minus15 0 15 30 45 60120572 (deg)

minus15 0 15 30 45 60minus1

minus05

0

05

1

15

2

CL

120572 (deg)minus15 0 15 30 45 60

minus1

minus05

0

05

1

15

2

CL

120572 (deg)



119871and 119862

119863




119871and


119871and 119862










to a higher 120572







119901




119901based on an







infin=



73 4 104 14910 244 350

111 4 159 22710 371 532

3 4 5 6 7 8 9 100000

0075

0150

0225

0300

0375

0450

Cp

120582












infin= 73ms The


119871maxof every


119901


119901by observing





111ms [1])




119901


119901was


119901curve














119901curve is







3 4 5 6 7 8 9 100000

0075

0150

0225

0300

0375

0450

Cp

120582

(a)

3 4 5 6 7 8 9 100000

0075

0150

0225

0300

0375

0450

Cp

120582

(b)

3 4 5 6 7 8 9 100000

0075

0150

0225

0300

0375

0450

Cp

120582

(c)

3 4 5 6 7 8 9 100000

0075

0150

0225

0300

0375

0450

Cp

120582

(d)






119901curveThe



119871as having a















0 1 2 3 4 5 6 7 8000

005

010

015

020

025

030

035

040

045

111ms104ms92ms

84ms73ms64ms

120582

Cp


infinrange of

64ms to 111ms [1]

3 4 5 6 7 8 9 100000

0075

0150

0225

0300

0375

0450

Cp

120582







5 Conclusions


3 4 5 6 7 8 9 100000

0075

0150

0225

0300

0375

0450

Cp

120582




3 4 5 6 7 8 9 100000

0075

0150

0225

0300

0375

0450

Cp

120582









119901gradually




Competing Interests


Acknowledgments


References

























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










minus15 0 15 30 45 60minus1

minus05

0

05

1

15

2

0

05

1

15

2

CL

CD


120572 (deg)

minus15 0 15 30 45 60120572 (deg)

0

05

1

15

2CD

minus15 0 15 30 45 60120572 (deg)

0

05

1

15

2

CD

minus15 0 15 30 45 60120572 (deg)

minus15 0 15 30 45 60minus1

minus05

0

05

1

15

2

CL

120572 (deg)minus15 0 15 30 45 60

minus1

minus05

0

05

1

15

2

CL

120572 (deg)



119871and 119862

119863




119871and


119871and 119862










to a higher 120572







119901




119901based on an







infin=



73 4 104 14910 244 350

111 4 159 22710 371 532

3 4 5 6 7 8 9 100000

0075

0150

0225

0300

0375

0450

Cp

120582












infin= 73ms The


119871maxof every


119901


119901by observing





111ms [1])




119901


119901was


119901curve














119901curve is







3 4 5 6 7 8 9 100000

0075

0150

0225

0300

0375

0450

Cp

120582

(a)

3 4 5 6 7 8 9 100000

0075

0150

0225

0300

0375

0450

Cp

120582

(b)

3 4 5 6 7 8 9 100000

0075

0150

0225

0300

0375

0450

Cp

120582

(c)

3 4 5 6 7 8 9 100000

0075

0150

0225

0300

0375

0450

Cp

120582

(d)






119901curveThe



119871as having a















0 1 2 3 4 5 6 7 8000

005

010

015

020

025

030

035

040

045

111ms104ms92ms

84ms73ms64ms

120582

Cp


infinrange of

64ms to 111ms [1]

3 4 5 6 7 8 9 100000

0075

0150

0225

0300

0375

0450

Cp

120582







5 Conclusions


3 4 5 6 7 8 9 100000

0075

0150

0225

0300

0375

0450

Cp

120582




3 4 5 6 7 8 9 100000

0075

0150

0225

0300

0375

0450

Cp

120582









119901gradually




Competing Interests


Acknowledgments


References

























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












infin=



73 4 104 14910 244 350

111 4 159 22710 371 532

3 4 5 6 7 8 9 100000

0075

0150

0225

0300

0375

0450

Cp

120582












infin= 73ms The


119871maxof every


119901


119901by observing





111ms [1])




119901


119901was


119901curve














119901curve is







3 4 5 6 7 8 9 100000

0075

0150

0225

0300

0375

0450

Cp

120582

(a)

3 4 5 6 7 8 9 100000

0075

0150

0225

0300

0375

0450

Cp

120582

(b)

3 4 5 6 7 8 9 100000

0075

0150

0225

0300

0375

0450

Cp

120582

(c)

3 4 5 6 7 8 9 100000

0075

0150

0225

0300

0375

0450

Cp

120582

(d)






119901curveThe



119871as having a















0 1 2 3 4 5 6 7 8000

005

010

015

020

025

030

035

040

045

111ms104ms92ms

84ms73ms64ms

120582

Cp


infinrange of

64ms to 111ms [1]

3 4 5 6 7 8 9 100000

0075

0150

0225

0300

0375

0450

Cp

120582







5 Conclusions


3 4 5 6 7 8 9 100000

0075

0150

0225

0300

0375

0450

Cp

120582




3 4 5 6 7 8 9 100000

0075

0150

0225

0300

0375

0450

Cp

120582









119901gradually




Competing Interests


Acknowledgments


References

























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










3 4 5 6 7 8 9 100000

0075

0150

0225

0300

0375

0450

Cp

120582

(a)

3 4 5 6 7 8 9 100000

0075

0150

0225

0300

0375

0450

Cp

120582

(b)

3 4 5 6 7 8 9 100000

0075

0150

0225

0300

0375

0450

Cp

120582

(c)

3 4 5 6 7 8 9 100000

0075

0150

0225

0300

0375

0450

Cp

120582

(d)






119901curveThe



119871as having a















0 1 2 3 4 5 6 7 8000

005

010

015

020

025

030

035

040

045

111ms104ms92ms

84ms73ms64ms

120582

Cp


infinrange of

64ms to 111ms [1]

3 4 5 6 7 8 9 100000

0075

0150

0225

0300

0375

0450

Cp

120582







5 Conclusions


3 4 5 6 7 8 9 100000

0075

0150

0225

0300

0375

0450

Cp

120582




3 4 5 6 7 8 9 100000

0075

0150

0225

0300

0375

0450

Cp

120582









119901gradually




Competing Interests


Acknowledgments


References

























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 1 2 3 4 5 6 7 8000

005

010

015

020

025

030

035

040

045

111ms104ms92ms

84ms73ms64ms

120582

Cp


infinrange of

64ms to 111ms [1]

3 4 5 6 7 8 9 100000

0075

0150

0225

0300

0375

0450

Cp

120582







5 Conclusions


3 4 5 6 7 8 9 100000

0075

0150

0225

0300

0375

0450

Cp

120582




3 4 5 6 7 8 9 100000

0075

0150

0225

0300

0375

0450

Cp

120582









119901gradually




Competing Interests


Acknowledgments


References

























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











119901gradually




Competing Interests


Acknowledgments


References

























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









Documents

Wind Turbine Performance in Controlled Conditions: BEM Modeling