Wind Turbine Post-Stall Airfoil 

Performance Characteristics 

Guidelines for Blade-Element 

Momentum Methods

Preprint 

October 2004 • NREL/CP-500-36900 

J. Tangler 

National Renewable Energy Laboratory

J. David Kocurek 

Computational Methodology Associates 

To be presented at the 43rd AIAA Aerospace Sciences 

Meeting and Exhibit 

Reno, Nevada 

January 10–13, 2005 

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1

Wind Turbine Post-Stall Airfoil Performance Characteristics 

Guidelines for Blade-Element Momentum Methods 

James L. Tangler 

National Renewable Energy Laboratory 

james_tangler@nrel.gov 

J. David Kocurek 

Computational Methodology Associates 

drtomcat@msn.com 

The objective of this study was to provide post-stall airfoil data input guidelines for the prediction of peak 

and post-peak rotor power when using blade-element momentum theory. A steady-state data set from the 

Unsteady Aerodynamic Experiment (UAE) rotor test was used to provide guidelines for the development of a 

global post-stall method for the prediction of post-stall 3-D airfoil characteristics to be used with 2-D airfoil 

data. Based on these UAE data, methods to emulate the 3-D aerodynamics in the post-stall region were 

explored. Also suggested are experimental tests needed to better understand the 3-D flow physics and to 

quantify needed theory or empirical factors for a global post-stall approach to support blade-element 

momentum methods. 

I. Introduction 

The prediction of peak rotor power and post-peak power is important in the design of constant-speed and variablespeed stall-regulated rotors. For small turbines, the latter approach is seen as a viable means of controlling peak 

power with power electronics in lieu of more expensive variable-pitch control or noise-producing rotor furling. 

Analytical and experimental studies1-16 have been directed toward understanding the complex 3-D flow physics that 

are associated with the post-stall region following peak rotor power. A shortcoming of the experimental studies has 

been the lack of a method for determining the blade’s angle of attack (α) distribution so that normal and tangential 

force coefficients (Cn and Ct) acquired from chordwise pressure measurements can be converted into lift and drag 

coefficients (Cl and Cd) for engineering calculations. 

Recent studies14-16 have addressed the need for determining the angle of attack distribution from experimental data. 

Under the sponsorship of the National Renewable Energy Laboratory (NREL) the Lifting-Surface Prescribed-Wake 

(LSWT) performance-prediction methodology17, provided a unique capability for deriving angle of attack. Unsteady 

Aerodynamic Experiment (UAE) Cn and Ct data could then be converted into values of Cl and Cd using angle of 

attack distributions derived from LSWT. Through an iterative process, agreement was achieved between UAEmeasured and LSWT-predicted Cn and Ct radial distributions. This agreement yielded angle of attack distributions 

compatible with the measured post-stall 3-D aerodynamic characteristics. Unlike blade-element momentum (BEM), 

the LSWT methodology accounts for the induced effects of the blade configuration and those from the span-wise 

distribution of trailing vorticity in calculating the angle of attack distribution14. 

Based on the UAE data in combination with LSWT-derived angle of attack distributions, the flow physics of 

inboard delayed stall was analyzed to determine how it manifests itself through enhanced Cl and Cd. An important 

finding was that a midspan, rapid-drag rise governed the peak power of the UAE rotor16. Significant speculation 

exists as to the sequence of aerodynamic events that culminate in this midspan rapid drag raise that governs peak 

power. 

Another finding14 was that after an angle of attack of 20 degrees the lift/drag ratio for the five radial locations at 

which pressure measurements were acquired essentially followed simple flat plate theory. These studies14-16 also 

illustrated again the difficulty of relating BEM-predicted angle of attack distributions to the post-stall 3-D 

aerodynamics and measured power. This finding pointed to the need for a global post-stall approach, as for 

instance, previously developed by Viterna18,19, for generating post stall Cl and Cd based on both airfoil and bladespecific stall characteristics. 
2

As a result of its simplicity, BEM is the most widely used theory for rotor design and analysis. Consequently, a 

need exists to provide better guidelines for establishing post-stall values of Cl and Cd that characterize the net blade 

aerodynamics. The present study explores and attempts to explain the 3-D aerodynamics that exists before and after 

peak rotor power. Further discussed is how these airfoil data characteristics relate to an inboard standing vortex 

(implied by the UAE measurements) followed by possible vortex bursting. With this understanding, the Viterna 

global post-stall approach was evaluated for various combinations of input parameters for predicting post-stall 

power. Guidance for the Viterna method input parameters was provided by UAE data and flat plate theory. This 

evaluation also included a sensitivity study of the required input parameters on the predicted power. 

II. UAE Rotor Steady State Tests 

As part of the UAE testing, steady-state data sets were acquired in the NASA Ames 24.4-m x 36.6-m (80-ft x 120-ft 

test section) wind tunnel. The rotor configuration was two-bladed, constant speed (72 rpm), upwind, and stall 

regulated. The 5.03-m (16.5-ft) rotor radius includes a tapered, twisted blade20 and hub (Fig. 1). The low maximum 

Cl, 21% thick, NREL S809 airfoil21 in Fig. 2 was used exclusively along the blade except for the cuff region, which 

transitioned from the circular root end fitting to the S809. 

 Values of Cn and Ct at the five spanwise stations (r/R = 0.30, 0.47, 0.63, 0.80, 0.95) were derived from 22 pressure 

taps per station. Measured Cn and Ct were converted to Cl and Cd using LSWT-derived angles of attack with the 

following equations: 

α

α α

α

2

t n

l

tan

1 1

sin tan

C tan C

C

+

+

= (Eq. 1) 

α

α

sin

C C cos C n l

d

− = (Eq. 2) 

The resulting power curves, acquired from lowspeed shaft torque measurements, at tip pitch 

angles of 2, 3, and 4 degrees toward feather with 

respect to the airfoil chord line, are the basis for 

this correlation between measured and predicted 

power. However, airfoil characteristics (α, Cl, Cd) 

used for all the predicted power curves in this 

study were derived only from data associated with 

the 3-degree blade pitch. 

III. Stall and Post-Stall Aerodynamics 

A blade circulation contour plot was previously 

calculated14 based on measured UAE Cn and Ct

data and LSWT-derived Cl for wind speeds up to 

16 m/s. Equation 3 was used to calculate

circulation at each radial station from the local 

values of chord (c) and relative velocity (V). 

Γ = 0.5cClV (Eq. 3) 

This equation, which is based on unseparated 

flow, is believed to be a useful, gross 

approximation of the circulation. Future, flow 

visualization studies are needed to better validate 

this assumption. 

Figure 1. Chord and twist distribution for the UAE 

Figure 2. S809 airfoil section force coefficients. 
3

From the circulation plot (Fig. 3) and local values of 

Cl and Cd, the sequence of related aerodynamic 

events that occur as the twisted/tapered rotor 

approaches peak power (Fig. 4) can be analyzed. 

At 8 m/s a spanwise standing vortex appears to build 

up over the inboard half of the blade with lift 

coefficients at 30% and 47% radius exceeding the 2-

D maximum of 1.0. At this wind speed the highest 

angle of attack occurs in the midspan region of the 

blade. Delayed stall effects, which drop off rapidly 

with radius, are minimal at midspan. Consequently, 

the first occurrence of local blade stall is between 

the wind speed of 8 m/s and 9 m/s at the blade’s 

midspan location for an angle of attack of 11 degrees 

as calculated by LSWT16 and illustrated in Fig. 5. 

This local stall region is thought to form a midspan 

endplate effect for the inboard standing vortex.22 

This endplate effect would likely force the inboard 

spanwise standing vortex into the streamwise 

direction. This abrupt change in direction of the 

vorticity could contribute to a vortex burst over the 

suction surface of the blade, which coincides with 

peak rotor power. 

Indirect evidence of a vortex burst is seen in the 

large local drag increase starting at 9 m/s (Fig. 6). 

Here, the drag coefficient, which exceeds 0.3 at 10 

m/s, is three times greater than the other four radial 

stations. The lift coefficient associated with the high 

drag at 47% radius shows a local region with little 

change. The large drag increase results in a local 

midspan power decrease that corresponds to peak 

rotor power.16 

IV. Application to Blade-Element 

Momentum 

Because of its simplicity BEM is the most widely 

used theory for rotor design and analysis.23 When 

used with accurate 2-D airfoil wind-tunnel data at 

angles of attack below stall, BEM provides 

reasonably accurate performance prediction. At 

moderate wind speeds, this capability has sufficed 

for blade geometry optimization for peak power 

coefficient. For the prediction of high wind speed 

peak rotor power, in the presence of local blade 

stall, BEM lacks the ability to model much of the 

flow physics that define the angle of attack 

distribution. Angle of attack distributions in the 

stall and post-stall regions are over predicted as a 

result of inadequate induced axial velocity. 

Insufficient induced axial velocity at the blade 

results from the uniform inflow assumption around each rotor annulus. In addition, the assumption of no interaction 

between adjacent rotor annuluses overlooks the midspan trailing vorticity that alters the local angle of attack. In the 

presence of blade stall, prescribed-wake or free-wake performance prediction methods have the potential to more 

0.30 0.47 0.63 0.80 0.95

7

8

9

10

11

12

13

14

15

16

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

m**2/sec.

r/R

Windspeed, m/s

3 degree blade pitch

Figure 3. Circulation contour distribution. 

Figure 4. Blade circulation at peak rotor power. 

5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

0.30

0.47

0.63

0.80

0.95

Angle of Attack

Windspeed, m/s

r/R

35-40

30-35

25-30

20-25

15-20

10-15

5-10

0-5

3 degree blade pitch

Figure 5. Angle of attack versus windspeed. 
4

accurately predict the blade’s angle of attack 

distribution. 

A global post-stall airfoil data synthesization 

method is needed to overcome the inability of BEM 

to accurately predict the angle of attack distribution 

in the presence of stall. Such an approach should 

be tailored to capture the net aerodynamic effects 

related to the blade geometry rather than detailed 

flow physics characteristic of vortex wake methods. 

V. Flat Plate Theory 

The lift-to-drag ratio (Cl/Cd) associated with flat 

plate theory provides a useful guide for nonrotating and rotating finite span wings at angles of 

attack following fully separated flow. For flat plate 

theory the variation of Cl, Cd and Cl/Cd versus angle 

of attack are shown in Fig. 7. 

At angles of attack of 20, 30 and 45 degrees, ideal 

flat plate theory results in Cl/Cd ratios of 2.75, 1.73, 

and 1.00, respectively. For non-rotating wings of 

different aspect ratios3

 the Cl/Cd ratio closely 

followed flat plate theory over the angle of attack 

range of 30 to 90 degrees. For the rotating UAE 

rotor the Cl/Cd ratio at the five radial stations, at 

which pressure measurements were acquired 

closely follow flat plate theory over the angle of 

attack range of 20 to 90 degrees (Fig. 8). Although 

flat plate theory provides guidance for the post-stall 

Cl/Cd ratios for angles of attack in the range of 20 to 

90 degrees, wind turbine power calculations are 

also dependent on the magnitude of the associated Cl and Cd. The magnitudes of these parameters at 20 degrees are 

airfoil and blade planform dependent. 

At 20 degrees the rapidly increasing drag dominates the Cl/Cd ratio. At 90 degrees, where the lift is close to zero, 

blade planform or aspect ratio effects dictate the drag. However, for very large wind turbine blades with airfoil 

thicknesses of up to 40 percent, airfoil thickness also becomes a factor in determining the drag at 90 degrees. The 

airfoil starts acting more like an ellipse than a flat plate. Non-rotating semi-span tests3

 found the maximum drag at 

90 degrees to decrease with airfoil thickness over the range of 9 to 18 percent for a given aspect ratio wing. 

VI. Global Post Stall Model 

For BEM, the Viterna method provides a convenient 

global approach to relate the post-stall Cl and Cd to the 

overall blade geometry rather than to the individual 

blade stations. Viterna used this post-stall approach to 

provide agreement between measured and predicted 

power for the Mod-0 and Mod-1 turbines.18 Although 

this method has been used for predicting post-stall airfoil 

characteristics, an incomplete understanding of the stall 

process existed at the time of its development. Based on 

the results from steady-state UAE measurements new 

guidelines are indicated for using the Viterna method. 

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0 5 10 15 20 25

Windspeed, m/s

Lift & Drag Coefficients

r/R=0.30, Cl

r/R=0.47, Cl

r/R=0.63, Cl

r/R=0.80, Cl

r/R=0.95, Cl

r/R=0.30, Cd

r/R=0.47, Cd

r/R=0.63, Cd

r/R=0.80, Cd

r/R=0.95, Cd

rapid drag increase

3 degree blade pitch

Figure 6. Cl and Cd versus wind speed. 

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0 30 60 90 120 150 180 210 240 270 300 330 360

alpha, deg.

Cl, Cd, Cl/Cd

Cl

Cd

Cl/Cd Cl=2sin(alpha)cos(alpha)

Cd=2(sin(alpha))^2

Figure 7. Flat plate theory Cl, Cd and Cl / Cd. 

0

5

10

15

20

25

12 15 18 21 24 27 30

Angle of attack, degrees

Lift/Drag

r/R=0.30

r/R=0.47

r/R=0.63

r/R=0.80

r/R=0.95

flat plate

UAE avg

Figure 8. UAE data and flat plate theory. 
5

The original Viterna equations shown below require an initial angle of attack (αstall) with its associated drag (Cd stall) 

and lift coefficient (Cl stall) along with a blade aspect ratio (AR). An important requirement is for the Viterna 

equations to satisfy flat plate theory. This condition is only satisfied when the Cl/Cd at the initial angle of attack 

agrees with flat plate theory. Otherwise, the Cl/Cd at higher angles will not agree with flat plate theory. In addition, 

results with the Viterna equations are largely dependent on the magnitude of the initial values of Cl and Cd. The 

blade AR selection is of lesser importance. The AR is needed for determining a maximum blade drag coefficient 

(Cd max) at 90 degrees. The AR selection has an effect on post peak power prediction at wind speeds around 20 m/s. 

A larger AR results in greater high wind speed lift, drag and power. In this study AR selection is based on a value 

that provides good correlation with UAE measured rotor power at 20 m/s. The Viterna equations are as follows: 

The choice of the airfoil’s stall or leading-edge 

separation angle of attack and associated drag strongly 

influence predicted power just after peak power. 

Viterna’s equations are based on using the airfoil stall 

angle at maximum Cl along with the associated 

maximum Cl and Cd. Another option is to use the 

leading-edge separation angle that corresponds to the 

local Cl minimum just after maximum Cl. For the 

S809 airfoil, the 2-D maximum Cl of 1.06 is seen to 

occur at 15 degrees and to have a value of 0.68 at 20 

degrees with full leading-edge separation. Associated 

2-D drag coefficients for these angles are 0.1 and 0.4, 

respectively. Unfortunately, neither one of these 

options provides a Cl/Cd for the initial condition of the 

Viterna equations that satisfy flat plate theory. 

For predicting performance with BEM, Viterna uses 

the Prandtl tip and hub loss model below stall. Above 

stall the tip and hub loss model is turned off because 

finite blade length effects are thought to be accounted 

for through the Viterna equations. In this study, better 

results were obtained with the tip and hub loss models 

used both below and above stall. Without the tip loss 

model, the tip loading is always too high. 

VII. Post-Stall Cl and Cd

Guidelines are needed to quantify the Cl and Cd over the angle of attack range from when the blade stalls to when 

flat plate theory takes over at 20 degrees. Blade-averaged values, based on UAE-derived values of Cl and Cd, appear 

appropriate at 20 degrees where flat plate theory begins. To obtain these values for the UAE blade required 

averaging the Cl and Cd for the five radial stations versus 

angle of attack. The averaging process required a unit span 

weighting. As a result of the favorable spanwise spacing, 

the 30, 47, 63, and 80 percent radial stations had a unity 

spanwise weighting factor, whereas the 95% station had a 

three-quarter spanwise weighting factor as a result of its 

close proximity to the tip. The average values of Cl and Cd

are shown in Fig. 9 relative to the five individual stations. 

As a result of inboard delayed stall effects, the average 

value of Cl increases beyond that of 2-D data at an angle of 

attack from 10 degrees to 20 degrees, where Cl avg. reaches 

a value of 1.24 at 20 degrees. Similarly, the Cd avg.

increases to a value of 0.44 at 20 degrees. These values 

provide a Cl/Cd ratio at 20 degrees that is in agreement with 

flat plate theory. 

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0 5 10 15 20 25 30

Angle of Attack, degrees

Lift & Drag Coefficients

r/R=0.30, Cl

r/R=0.47, Cl

r/R=0.63, Cl

r/R=0.80, Cl

r/R=0.95, Cl

Cl average

Cd average

r/R=0.30, Cd

r/R=0.47, Cd

r/R=0.63, Cd

r/R=0.80, Cd

r/R=0.95, Cd

3 degree blade pitch

Figure 9. Blade average Cl and Cd relative to 

individual radial stations. 

C 1.11 0.018AR dmax = + ( ) α = 90° (Eq. 4) 

C B sin α B2 cosα 2

d = 1 + ( ) α = 15°to90° (Eq. 5) 

where: 

B1 = Cdmax (Eq. 6) 

stall

stall

2

dstall dmax

2

cos

C C sin

B

α

− α = (Eq. 7) 

α

α

α

sin

cos C A sin 2 A

2

l = 1 + 2 ( ) α = 15°to90° (Eq. 8) 

where: 

A1 = B1 / 2 (Eq. 9) 

( ) 2 l stall dmax stall stall A = C − C sinα cosα

stall

2

stall

cos

sin

α

α (Eq. 10) 
6

The blade averaged values (Cl avg.=1.24 and Cd avg.=0.44) are now used as inputs for the Viterna equations along with 

a torque weighted blade AR=11.0. This simplified weighted aspect ratio results from the blade radius divided by the 

local chord at 80% radius. Subsequent calculations showed that an AR of 14 provided better agreement with the 

measured power from 16 m/s to 22 m/s. This implies that if a torque rated aspect ratio of 11.0 is used in Eq. 4 the 

constant 0.018 should be increased to 0.023. Further study is needed to better adapt Eq. 4 for different blade 

geometries. Resulting Viterna predicted Cl and Cd for an AR of 14 are shown in Fig. 10 for the angle of attack range 

of 20 to 90 degrees along with the pre flat-plate values of Cl avg. and Cd avg.. At 45 degrees, the Cl/Cd ratio passes 

through 1.0, which satisfies flat plate theory, and the blade maximum drag coefficient at 90 degrees is 1.31. 

VIII. Predicted Rotor Power 

A comparison of UAE rotor measured and predicted 

power is shown in Fig. 11 for blade tip pitch angles 

of 2, 3, and 4 degrees. Predicted power is based on 

2-D Delft data21, shown in Fig. 10, up to the stall 

angle of attack of 9.21 degrees. For larger angles of 

attack, the higher, Cl avg. data was used up to the flat 

plate data angle of 20 degrees, where the Viterna 

equations were implemented. Steady-state measured 

power was derived from low speed shaft torque 

strain gages. 

The predicted rotor power is calculated using 

NREL’s WT_Perf BEM performance prediction 

code for an equally spaced, 20 segment blade.24 In 

this report the Prandtl tip and hub loss were 

employed throughout the turbine calculation range. 

A case can be made to turn off the tip and hub loss 

model when airfoil input data are derived from 

experimental results and the Viterna method is used 

after 20 degrees. However, without a tip and hub 

loss model the peak power at 9 m/s is over predicted 

and the post-peak power is under predicted up to 17 

m/s. 

Using Delft 2-D data predicted results are in 

excellent agreement with measurements over the 

linear part of the power curve from 5 m/s to 8 m/s 

for all three pitch angles. Reasonable agreement is 

seen over the wind speed range of 9 m/s to 25 m/s 

using the post stall UAE-averaged airfoil data and 

the Viterna equations starting at 20 degrees. The 

biggest deviation is the under prediction of peak 

power at 9 m/s where UAE derived drag data 

indicate a rapid drag increase at 47% radius. The 

airfoil Cl avg. appears to be insufficient for inboard 

stations to adequately contribute to peak rotor 

power. Agreement at 20 m/s is influenced by the 

input AR for the Viterna equations. For the UAE 

rotor, an aspect ratio of 14.0 provided the best 

agreement in predicted rotor power from 16 to 22 

m/s. 

A sensitivity study of the Viterna equations to a change in input parameters was conducted. As shown in Fig. 12, 

the aspect-ratio selection dictates the maximum drag coefficient and governs the predicted power at high wind 

speeds over 15 m/s. Power calculations were done for the torque weighted aspect ratios of 11, 14, and 17. The 

-1.0

0.0

1.0

2.0

3.0

4.0

-10 0 10 20 30 40 50 60 70 80 90

Alpha, deg

Cl, Cd, L/D

UAE Cl avg, Viterna, AR=14

UAE Cd avg, Viterna, AR=14

UAE L/D avg 

Cl 2-D Delft data

Cd 2-D Delft data

L/D Viterna

L/D Flat Plate

Figure 10. S809 airfoil data input for WT_Perf. 

0

2

4

6

8

10

12

14

0 5 10 15 20 25 30

Wind Speed, m/s

Rotor Power, kW

2 deg, measured

3 deg, measured

4 deg, measured

Viterna, AR=14, Cd=.441

Viterna, AR=14, Cd=.441

Viterna, AR=14, Cd=.441

Delft 2D data to stall, UAE average data to 20 deg., Viterna post 

stall after 20 deg., tip/hub loss on for all wind speeds

Figure 11. Comparison of UAE measured and predicted 

power. 
7

predicted power at 25 m/s increased 2% by increasing 

the AR by an increment of three. At this wind speed, 

most of the blade is in the angle of attack range of 35 to 

45 degrees. 

For the Viterna equation inputs at 20 degrees, a 10% 

increase or decrease in simultaneous input values of Cl

and Cd results in a continuous increase or decrease in the 

post-stall predicted power from 10 m/s to 25 m/s as seen 

in Fig. 13. At 25 m/s this change in power is about plus 

and minus 5% relative to the baseline, 3-degree blade 

pitch. 

The under predicted peak power at 9 m/s is still 

dependent on the averaged UAE airfoil data prior to the 

Viterna equations. These results also illustrate that the 

post-stall bucket in the power curve is strongly 

dependent on choosing the correct values of Cl and Cd at 

20 degrees. Halfway along the post-stall wind speed 

range, where a local minimum in power exists at 17.5 

m/s, the blade angle of attack distribution lies in the 20 

to 35 degree range for the 3-degree blade pitch. 

IX. Standing Vortex Induced High Lift 

The inboard delayed stall high-lift effect is only partially 

captured in the averaged S809 airfoil data. Based on the 

correlation between predicted and measured power a 

deficiency in predicted power still exists just before peak 

power. This deficiency is not accounted for in the 

averaged airfoil data and is thought to be the result of 

additional lift from an inboard standing vortex located 

between the measured pressure distribution stations at 

30% and 47% radius. Measurements from the individual 

4% chordwise transducers (Fig 14), which provide 

intermediate point measurements at 36% and 41% 

radius, show the suction pressure coefficient to be 

greatest between these stations. 

When the averaged airfoil data is enhanced for the three 

blade segments between 30% and 45% radius, as seen in 

Fig. 15, predicted power agrees closely with 

measurements between 8 m/s to 10 m/s, as shown in Fig. 

16. To achieve this agreement the lift curve slope for 

these segments has to be increased to 0.3 Cl/deg relative 

to a 2-D value of 0.1 Cl/deg. The UAE derived lift curve 

slope for the 30% radial station has been found to be of 

similar or greater magnitude. This high lift curve slope 

is used over the angle of attack range of 8 to 13 deg, and 

then it drops linearly to UAE-averaged Cl at 16 degrees. 

This limited angle of attack range is thought to 

correspond to where the influence of the spanwise standing vortex is greatest followed by a vortex burst that results 

in a rapid Cl drop off at higher angles. No adjustment to the averaged drag is implemented since the averaged values 

are thought to be somewhat adequate, but low. 

0

2

4

6

8

10

12

14

0 5 10 15 20 25 30

Wind Speed, m/s

Rotor Power, kW

2 deg, measured

3 deg, measured

4 deg, measured

AR=11, Viterna

AR=11, Viterna

AR=11, Viterna

AR=14, Viterna

AR=14, Viterna

AR=14, Viterna

AR=17, Viterna

AR=17, Viterna

AR=17, Viterna

Figure 12. Aspect ratio sensitivity. 

0

2

4

6

8

10

12

14

0 5 10 15 20 25 30

Wind Speed, m/s

Rotor Power, kW

4 deg, measured

3 deg, measured

2 deg, measured

AR=14 Cd=.440

AR=14, Cd=.440

AR=14, Cd=.440

AR=14, Cd=.484

AR=14, Cd=.484

AR=14, Cd=.484

AR=14, Cd=.396

AR=14, Cd=.396

AR=14, Cd=.396

Figure 13. Viterna input Cl and Cd sensitivity. 

5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

30

36

41

47

52

58

63

69

74

80

85

90

92

95

98

Windspeed, m/s

Radius, %

-2.75--2.5

-2.5--2.25

-2.25--2

-2--1.75

-1.75--1.5

-1.5--1.25

-1.25--1

-1--0.75

-0.75--0.5

-0.5--0.25

-0.25-0

0-0.25

3 degree blade pitch

Figure 14. Pressure coefficient contour at 4% chord. 
8

The use of 2-D post-stall Delft airfoil data would require a greater amount of stall delay (increased Cl and Cd) over a 

larger angle of attack range since no 3-D delayed stall effects are present in the 2-D data as there are in the UAE 

averaged airfoil data. 

X. Conclusion 

Delft 2-D wind tunnel data up to stall, followed by steady-state UAE-average post-stall airfoil data, and the Viterna 

equations guided by flat plate theory, were used with BEM theory to predict the power curve for the Phase VI UAE 

rotor. Agreement between measured and predicted power, using UAE average post-stall airfoil data, guided the 

choice of input parameters to be used with the Viterna separated flow airfoil data synthesization method. 

Delft 2-D wind tunnel data provided excellent agreement between predicted and measured power up to a wind speed 

of 8 m/s. A simulated, local, inboard standing vortex with high induced-lift over the angle of attack range of 8 to 13 

degrees was required to achieve peak power agreement for the wind speed range of 8 m/s to 10 m/s. Using UAE Cl 

avg. and Cd avg. data at an angle of attack of 20 degrees resulted in good agreement with measured post stall power. 

Predicted post-stall power was relatively sensitive to the Viterna equation inputs of Cl avg and Cd avg at 20 degrees and 

less sensitive to the AR value. Predicted high wind speed power from 16 m/s to 22 m/s was adjusted with the blade 

AR input to agree with measured power. The Viterna method needs to be implemented after leading-edge 

separation and the Cl/Cd ratio for the initial conditions needs to agree with flat-plate theory. 

Rotating blade, post-stall flow visualization is needed to help bridge the gap from 2-D airfoil data to the Viterna 

method and to better understand the midspan 3-D flow physics. The use of a water towing tank and a small-scale 

wind turbine emitting colored dye is a plausible experimental approach and should be explored for steady-state flow 

visualization of an inboard standing vortex and possible vortex bursting. 

Acknowledgments 

This work was supported by the U.S. Department of Energy. The assistance of L. J. Fingersh in preparing the UAE 

data is gratefully acknowledged.

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0.0

0.5

1.0

1.5

2.0

2.5

0 5 10 15 20 25 30

Angle of Attack, degrees

Lift Coefficient

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Wind Turbine Post-Stall Airfoil Performance Characteristics 

Guidelines for Blade-Element Momentum Methods: Preprint 

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14. ABSTRACT (Maximum 200 Words)

The objective of this study was to provide post-stall airfoil data input guidelines for the prediction of peak and postpeak rotor power when using blade-element momentum theory. A steady-state data set from the Unsteady 

Aerodynamic Experiment (UAE) rotor test was used to provide guidelines for the development of a global post-stall 

method for the prediction of post-stall 3-D airfoil characteristics to be used with 2-D airfoil data. Based on these UAE 

data, methods to emulate the 3-D aerodynamics in the post-stall region were explored. Also suggested are 

experimental tests needed to better understand the 3-D flow physics and to quantify needed theory or empirical 

factors for a global post-stall approach to support blade-element momentum methods. 

15. SUBJECT TERMS

wind energy; wind turbine; airfoil; airfoil performance; blade-element momentum 

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