Investigation of High Reynolds Number Effects on Rotor Blades for Wind Turbines

Staffan Wallmann

EUROS GmbH, Berlinwallmann@euros.de

Abstract

The increasing size of wind turbines leads to higher Reynolds numbers caused by a larger chord length. This work presents a method to modify measured, two-dimensional airfoil properties (Re = 3 M) to account for high Reynolds numbers (3 M < Re < 9 M) by using a calculated Reynolds number trend. The airfoil properties for high Reynolds numbers are characterised by an increased maximum lift, less frictional drag and a changed width of the low drag bucket. In a second step, aerodynamic and aero-elastic simulations of wind turbine characteristics are performed for a reference wind turbine of the 3 MW class. The Blade Element Momentum (BEM) calculations are based on the modified airfoil properties for high Reynolds numbers. The effect on the performance of wind turbines is positive, because the convenient operating range of the airfoils becomes wider. The optimum pitch angle of the rotor blade and the optimum tip speed ratio are increased due to the high Reynolds number effect. However, the better efficiency of the rotor also involves higher loads. The increased efficiency, as well as the increased loads, can be significant but is moderate for the reference wind turbine.

1. Introduction

The design of a large wind turbine can partly be derived from an existing smaller wind turbine. Known characteristics of the smaller turbine can be copied to the new turbine using

Christoph Klein

EUROS GmbH, Berlinklein@euros.de

the Law of Similarity [1]. Accordingly, the following parameters have to remain unchanged.

Number of blades

Tip speed ratio

Geometric proportions of blades

Materials

Airfoils (and their characteristics)

Aerodynamic and centrifugal forces increase by the square of the rotor radius, while gravity forces increase by the cube of the radius. Since the blade cross-sections also increase by the square of the radius, higher stress only results from gravity forces. This fact limits the size of wind turbines and has to be compensated by the use of lightweight construction. However, in terms of aerodynamics, keeping the airfoils unchanged does not necessarily result in unchanged airfoil properties. The reason therefore is the Reynolds number effect. Airfoil properties depend on the Reynolds number, because it indicates the dynamic similarity of two flow conditions. Increasing the rotor diameter leads to increased chord length and thus to increased Reynolds numbers. Hence airfoil properties, which are valid for small rotor blades, are not generally accepted for large rotor blades.

This work investigates the changes of airfoil properties due to the high Reynolds number effect (Re > 3 M) and studies the consequences for wind turbine characteristics.

x 106

8

Re7

6Vrel cSectionChord

NumberRe Velocity .Length

5Kinematic Viscosity

4

Reynolds

3Ordinary Reynolds number of measured airfoil properties: Re = 3 M

2Local Reynolds numbers at:

Cut Out Wind Speed

1Rated Wind Speed

Cut In Wind Speed

00.10.20.30.40.50.60.70.80.91

0

Radius r/R

Figure 1: Local Reynolds number on the reference rotor blade EU100 at various operating conditions. The local Reynolds number only depends on the section velocity, Vrel and the respective chord length, c at constant kinematic viscosity, .

For that purpose aerodynamic and aero-elastic simulations were carried out for a rotor blade of a reference wind turbine of the 3 MW class. The Reynolds number distribution over the blade length is illustrated in Figure 1 for three operating conditions in the wind speed range of 3 to 25 m/s. Particularly, the outer part of the blade operates at high Reynolds numbers of more than 7 M at rated wind speed. The properties of the airfoils of the reference rotor blade have been measured in a wind tunnel at Re = 3 M. Hence deviations between measured airfoil properties and the real application are expected. Since three-quarters of the power is generated with the outer half of the blade, a change of airfoil properties on this part is important to the performance of the rotor. A change of aerodynamic forces on the outer part of the blade is also important for the loads in the blade root because of the long lever arm.

A fundamental dependency of the wind turbine performance, particularly the maximum power coefficient and the optimum tip speed ratio, is shown in [2]. A blade design optimization for different Reynolds numbers verified that the solidity and the twist distribution generally depend on the Reynolds number too.

High Reynolds number airfoil properties are needed to consider the specific Reynolds number effect in wind turbine design and analysis. The Reynolds number in wind tunnel measurements usually does not exceed 3 to 4 M, because much effort is required to achieve higher Reynolds numbers. The approach in this work is to generate airfoil

coefficients for high Reynolds numbers synthetically on the basis of data measured at Re = 3 M and a calculated Reynolds number trend. Subsequently the synthetic airfoil data is used as input for steady state calculations and aero-elastic wind turbine simulations. The results are reviewed in comparison to calculations for the hypothetical case that there would be no Reynolds numbers effect.

2. Reynolds number effects on airfoil properties

A recent measurement of airfoil properties at high Reynolds numbers has been carried out in the Langley Low Turbulence Pressure Wind Tunnel for the 17% thick S825 airfoil of the NREL airfoil family [3]. Measured characteristics at Re = 1 to 6 M are presented in Figure 2.

The effects caused by increased Reynolds numbers are as follows.

Increased maximum lift and shift to higher angle of attack.

Reason: a higher share of inertial forces enables the boundary layer to stay attached longer in an adverse pressure gradient. Therefore the stall angle of attack is shifted to higher values and hence the maximum lift is increased.

Decreased drag.

Reason: viscous forces have less influence for increased Reynolds Numbers. Hence the friction drag is decreased.

Figure 2: Measured airfoil properties of the S825 section at various Reynolds numbers [3]

Decreased width of laminar bucket1.

Reason: transition occurs earlier for high Reynolds Numbers. The laminar bucket ends at angle of attacks, where the transition location rapidly moves towards the leading edge. This effect is shifted to lower angle of attacks for high Reynolds Numbers, hence the laminar bucket becomes smaller2. Increased width of low drag bucket3. Reason: the high drag outside the low drag bucket is generated by separated flow. The separation is shifted to higher angle of attacks and hence the drag is lower for a wider range of angle of attacks.

Slightly steeper lift-curve slope.

Steeper lift decrease after reaching of maximum lift.

Increase of lift to drag ratio, shift to smaller angle of attacks.

Increase of pitching moment at high angles of attack.

These changes of airfoil properties for an increased Reynolds number are confirmed by other high Reynolds number measurements, e.g. in [4] and [5].

3. Modification of airfoil properties

Airfoil properties for high Reynolds numbers are necessary to investigate the high Reynolds number effect on wind turbines. They can, for example, be calculated by the panel code RFOIL, which is a modification of the well known code XFOIL [6]. Figure 3 shows the calculated airfoil properties of the EU210 airfoil for the Reynolds number of 3, 6

and 9Mand the measured properties at

Re = 3M.Comparing the calculated and

measured airfoil properties leads to the fact that the measured maximum lift is lower and occurs at lower angles of attack (dotted red curve) as predicted by RFOIL for the same Reynolds number (solid red curve). The shape of the curve around maximum lift differs but the linear part of the lift curve is well predicted. However, the drag is generally underestimated by RFOIL. Considering the calculated airfoil properties for different Reynolds numbers in Figure 3, a trend is visible which is analogue to the trend observed in the high Reynolds number measurements (see part 2).

The conclusion from the above considerations is that the Reynolds number trend may be predicted well by RFOIL, although the absolute values slightly differ from measurements. Hence RFOIL calculations cannot replace the measured airfoil properties, but can be used to modify the measured airfoil properties to account for the Reynolds number trend. This is done by isolating the main Reynolds number effects of the calculated airfoil properties listed in part 2 (first four items) and including them to the measured airfoil properties. Thus, synthetic airfoil properties for high Reynolds numbers are generated. The detailed method for modifying the lift and drag coefficients is described in [7]. The general approach and result is visible in Figure 4, which presents the airfoil properties of the EU210 airfoil for different Reynolds numbers, once from RFOIL calculations and once the measured and synthetic airfoil properties. The Reynolds number trend predicted by RFOIL can be

EU210

Cl

AirfoiltypeRe

EUROS Measured 3 M

RFOIL Calculated3 M

RFOIL Calculated6 M

RFOIL Calculated9 M

[]

Cd

Figure 3: Measured and calculated airfoil properties of the EU210 for various Reynolds numbers

1 laminar bucket: range of particularly low drag due to a high share of laminar flow

2 The for wind turbines less relevant lower end of the laminar bucket is shifted to higher angle of attacks

3 low drag bucket: range of low drag because of mostly attached flow (includes laminar bucket)

d

n

re

eT

R

Measured

l

C

Calculated

[]

d

n

re

eTMeasured

R

Calculated

l

CRe Trend

Cd

Measured

l C

Synthetic =

Measured + Re Trend

Re = 9 M []

Re = 6 M

Re = 3 M

Measured

l

C

Synthetic =

Measured + Re Trend

Cd

Figure 4: Generation of synthetic airfoil properties. Transfer of the Reynolds number trend from airfoil properties calculated by RFOIL to measured airfoil properties.

found directly in the synthetic airfoil properties, but the general characteristics of the curves are similar to the measured airfoil properties. Hence the Reynolds number trend is captured well in the synthetic airfoil coefficients, as long as RFOIL predicts the Reynolds number trend well.

4. Verification of the method

Two measurements of airfoil properties at high Reynolds numbers [4] and [3] are used to verify the method for the generation of the synthetic airfoil properties (see Figures 5 and 6). The lift and drag coefficients which are measured at Re = 3 M (solid red curves) are modified by a Reynolds number trend which is calculated by RFOIL for the respective airfoil. Thus synthetic airfoil properties for high Reynolds numbers are generated (dashed curves) and presented in comparison to the

NACA64618

a) Langley Measurement Re = 3 M b) Langley Measurement Re = 6 M c) Langley Measurement Re = 9 M d) RFOIL Trend 3 -> 6 M applied to a) e) RFOIL Trend 3 -> 9 M applied to a)

measured high Reynolds number airfoil properties (blue and green solid curves).

Comparing the measured and synthetic drag curves of both airfoils leads to the conclusion that the drag coefficient is predictable. However, the prediction of the maximum lift increase shows some deviations. In the case of the NACA64618 (Figure 5), the maximum lift increase is underestimated by the synthetic airfoil properties while it is slightly overestimated in the case of the S825 airfoil (Figure 6). Nevertheless the use of the synthetic airfoil coefficients for wind turbine calculations is more appropriate than using low Reynolds number airfoil data. The advantage of this method is that there is reasonable airfoil data available at a time before wind tunnel tests at high Reynolds numbers are carried out.

Cl

1.5

1.2

0.9

0.6

0.3

0.0

-0.3

-10-50510152000.0040.0080.0120.0160.020.024

[]Cd

Figure 5: Comparison of measured [4] and synthetic airfoil properties of the NACA64618 airfoil

Cl

S8251.5

1.2

0.9

0.6

0.3

0.0

a) Langley Measurement Re = 3 M-0.3

b) Langley Measurement Re = 6 M

c) RFOIL Trend 3 -> 6 M applied to a)

-10-50510152000.0040.0080.0120.0160.020.024

[]Cd

Figure 6: Comparison of measured [3]5 and synthetic airfoil properties of the S825 airfoil

5. Effects of high Reynolds numbers on wind turbines

Steady state calculations and aero-elastic simulations were performed to study the Reynolds number effect on wind turbines. The calculations are based on the Blade Element Momentum Theory (software GH Bladed). The synthetic airfoil properties for high Reynolds numbers have been used in comparison to calculations with the ordinary airfoil data for Re = 3 M. Generally, the performance is increased for high Reynolds numbers. Figure 7 shows the power curve for the ordinary (coloured) and high Reynolds number calculations (black). The power performance of the rotor is increased for high Reynolds numbers and this effect is particularly important at low tip speed ratios and hence at rated power.

However, the Reynolds number effects are moderate for the considered rotor blade. The reason therefore can be seen in Figure 8 and 9, which present the dimensionless coefficients of the rotor. The power coefficient is increased for high Reynolds numbers at most tip speed ratios, but the rotor blade operates only in the range where the differences are very small. If the tip speed ratio at rated power were lower, the wind turbine would benefit significantly from the increased power coefficient due to the Reynolds number effect. For example, this would be the case if the rotor would be used on a turbine with higher nominal power. The reason for the increased efficiency is the increased maximum lift of the airfoils and the shift to higher angles of attack.

Power Curve and Rotor Speed

TipSpeedRatio

Rotor Speed

Electrical Power

Shaft Power

Rotor Speed

Tip Speed Ratio

High RN Calculation

15

12

9

6

3

Rated Power at V=11.4 m/s for ord. RN V=11.3 m/s for high RN

opt. TSR up to

V=9.7 m/s for ord. RN V=9.2 m/s for high RN

3000

2500

2000

1500

1000

500

Power [kW]

3691215182124Wind Speed [m/s]

Figure 7: Power curve and control variables of the reference rotor for ordinary (coloured) and high (black) Reynolds numbers (RN). The Tip Speed Ratio (TSR) is increased in the variable speed mode and hence the tip speed limitation starts at lower wind speed. Rated power is reached earlier due to the slightly better efficiency for high Reynolds numbers.

Power CoefficientcPcT

0.551.0

0.50Opt. TSR0.9

0.45Rated0.8

0.400.7

0.350.6

Ordinary Reynolds Numbers

0.30Optimum Blade Set Angle0.5

High Reynolds Numbers

Same Blade Set Angle

56789101112

Thrust Coefficient

Opt. TSR

Rated

56789101112

Tip Speed RatioTip Speed Ratio

Figure 8: Power and thrust coefficients of the reference rotor for ordinary (red) and high Reynolds Numbers (blue) with equal blade set angle.

Power CoefficientcPcT

0.551.0

0.50Opt. TSR0.9

0.45Rated0.8

0.400.7

0.350.6

Ordinary Reynolds Numbers

0.30Optimum Blade Set Angle0.5

High Reynolds Numbers

Optimum Blade Set Angle (Increased)

56789101112

Thrust Coefficient

Opt. TSR

Rated

56789101112

Tip Speed RatioTip Speed Ratio

Figure 9: Power and thrust coefficients of the reference rotor for ordinary (red) and high Reynolds numbers (blue). The blade set angle of the high Reynolds number coefficients is optimized (increased).

The thrust coefficient is also increased at low tip speed ratios. This holds the risk of increased loadings due to the Reynolds number effect. In Figure 9, the coefficients of the high Reynolds number calculations are presented for an optimised blade set angle. The best lift to drag ratio of the airfoils at high Reynolds numbers occurs at lower angles of attack. Therefore the optimum blade set angle is increased for high Reynolds numbers. The thrust coefficient is generally lower for higher pitch angles. As a result, the increased thrust coefficient at rated power can partly be compensated by adjusting the blade set angle to the optimum value for high Reynolds numbers.

The Reynolds number effects are particularly important at low tip speed ratios, e.g. in gusts. Dynamic simulations of gusts at various mean wind speeds and are presented in Figure 10. The rise of the wind speed (blue) leads to a decrease of the tip speed ratio (dark blue). The response of the wind turbine control to the gusts, particularly the pitch angle (dark

green), is different for the ordinary and high Reynolds number simulation. The flapwise bending moment (red) is slightly increased in gusts due to the Reynolds number effect.

Summary of high Reynolds number effects on wind turbines are as follows.

1. The maximum power coefficient CP.max is increased. This is caused by a lower drag in the low drag bucket, which leads to less profile losses and thus a power coefficient which is closer to the theoretical maximum of CP = 0.59.

2. The power coefficient at low tip speed ratios is increased. This is because more lift can be generated due to the higher maximum lift caused by the Reynolds number effect. Also less blade sections operate in stalled conditions which results in less drag. Hence profile losses are decreased at low tip speed ratios as well.

Power Production and Gust at four different hub wind speeds

[m/s]25Wind Speed

20

15

V

10

T [kNm]60Gen. Torque25

4015

20Pitch Angle[]

5

12

[rpm]15

12.5Tip Speed Ratio8

[-]

n10Rotor Speed4

P [MW]3Power

2

1

5Flapwise Bending Moment+ 3.2%

[kNm]4

3

2

My

1

0

051015 | 051015 | 051015 | 051015

Simulation Time [s]

Figure 10: Simulation of four gusts at different mean wind speeds displayed in series. Ordinary Reynolds number calculations (coloured) are compared to high Reynolds numbers (black).

3. The shape of the power coefficient curve changes, its saddle becoming wider. This is a consequence of points 1 and 2 above. This is advantageous for operating conditions at non-optimum tip speed ratios, namely for operation at maximum tip speed below rated power.

4. The optimum blade set angle is increased, because the best lift to drag ratio is shifted to smaller angles of attack and thus smaller lift coefficients. Hence the optimum performance is reached at smaller section inflow angles which are achieved by increasing the blade set angle.

5. The optimum tip speed ratio is increased. With this, the optimum lift to drag ratio occurs at smaller angles of attack and hence at smaller lift coefficients. The decrease in lift coefficient is compensated by increasing the section velocity, which shifts the optimum tip speed ratio to higher values.

6. The thrust coefficient is increased at low tip speed ratios, but can be partly decreased by increasing the blade set angle (see item 4 above).

6. Conclusion

In this work the effects of high Reynolds numbers (Re > 3 M) on airfoil properties have been investigated. The main effects are increased maximum lift and a shift to a higher angle of attack, decreased drag, decreased width of the laminar bucket and increased width of the low drag bucket. The airfoil analysis code RFOIL is generally capable of predicting this Reynolds number trend. A method has been developed to transfer the trend predicted by RFOIL to measured airfoil properties. Thus synthetic airfoil properties for high Reynolds numbers have been generated for the EUROS airfoil family. Validation of the method with experimental data shows good agreement for the drag modification. However, the prediction of the increased lift and stall angle of attack is potentially less precise, but the general trend of increased lift and stall angle of attack is reasonably predictable. Hence, the method for the modification of airfoil properties for high

Reynolds numbers can be used to improve the accuracy of wind turbine performance and loading calculations, when measured high Reynolds number airfoil data are not available.

Steady state and non-steady state performance and loading calculations have been carried out for a reference wind turbine of the 3 MW class. Here the synthetic airfoil characteristics have been applied. The effect of high Reynolds numbers on the performance of a wind turbine is generally positive. At fixed rotor speed below rated power, where the turbine operates at low tip speed ratios, there is significant better efficiency. This increase in efficiency is a consequence of the increased lift of the airfoils at high angles of attack. At low tip speed ratios, the blade cross sections operate mainly between the best lift to drag ratio (or just below) and maximum lift. Since the angle of attack of the best lift to drag ratio is decreased and the stall angle of attack is increased for high Reynolds numbers, the convenient operating range becomes wider. A wider operating range of the airfoils allows a wider operating range at fixed rotor speed and hence a higher maximum power (higher rotor rating) of the wind turbine. Turbines at particularly windy locations (such as those offshore) benefit from this. In the case of the rotor blade reference rotor blade, the Reynolds number effect could possibly enable the use on a wind turbine with higher rated power at windy sites.

The efficiency at the optimum tip speed ratio is slightly increased as well. The reason being that profile losses are reduced for high Reynolds numbers. Since the best lift to drag ratio occurs at lower angles of attack, the optimum blade set angle for maximum energy yield is increased. A positive side effect from this is that loadings are generally decreased for higher blade set angles. It has to be considered that a higher blade set angle, and hence a lower design angle of attack, results in operation at lower lift at optimum tip speed ratio. This has to be compensated by increasing the tip speed ratio or increasing the chord length.

High Reynolds numbers increase the loading of wind turbines when the rotor blade operates near or above the stall angle of attack. This is due to the increased lift of the airfoils, which increases the thrust force and hence the blade root bending moment. The increase of the bending moment of the reference rotor blade is relatively moderate because the lift increase does not occur on

the entire rotor blade at the same time. In the case of the reference rotor blade, a blade set angle optimised for high Reynolds number can compensate the higher steady state bending moment at rated wind speed. Since the increased blade set angle was not accounted for in the design of the reference rotor blade, the increased bending moment is not compensated in the current blade setting. However, the blade root bending moment is only increased slightly and is certainly catered for by the safety factors applied in the design.

References

[1] Gasch, R. und J. Twele (Hrsg.), Windkraftanlagen, Wiesbaden : B. G. Teubner Verlag / GWV Fachverlage GmbH, 2005. Bde. 4., vollst. berarb. und erw. Auflage.

[2] Cuerva, Alvaro, Reynolds Nuber Implications on the Determination of Wind Turbine Optimum Rotors, EWEC, 2009

[3] Somers, D.M., Design and Experimental Results for the S825 Airfoil, NREL/SR-500-36346, January 2005

[4] Abbott, Ira H., Doenhoff, Albert E. von and Stivers, Lois S. Jr., Summary of Airfoil Data, NACA Report No. 824, Langley Memorial Aeronautical Laboratory, 1945

[5] Somers, Dan M. and Tangler, James L., Wind-Tunnel Tests of Two Airfoils for Wind Turbines Operating at High Reynolds Numbers, Presented at the AIAA Wind Energy Meeting, NREL/CP-500-27891, January 2000

[6] Rooij, R.P.J.O.M. van, Modification of the boundary layer calculation in RFOIL for improved airfoil stall prediction, Report IW-96087R, Delft, September 1996

[7] Wallmann, S., Investigation of High Reynolds Number Effects on Rotor Blades for Wind Turbines, Diploma Thesis, Technical University of Berlin, April 2010