Navier–Stokes Predictions of the NREL Phase VI Rotor in the NASA Ames 80 ft ð 120 ft Wind Tunnel

WIND ENERGYWind Energ. 2002; 5:151–169 (DOI: 10.1002/we.64)

Research Article

Navier –Stokes Predictions of theNREL Phase VI Rotor in the NASAAmes 80 ft ð 120 ft Wind TunnelN. N. Sørensen,∗ Wind Energy Department, Risø National Laboratory, DK-4000 Roskilde,DenmarkJ. A. Michelsen, Department of Mechanical Engineering, Technical University of Denmark, DK-2800 Lyngby, DenmarkS. Schreck, National Renewable Energy Laboratory, 1617 Cole Boulevard, Golden, CO 80401,US

Key words:Navier–Stokes;computationalfluid dynamics;wind turbineaerodynamics;NREL Phase VI

This article describes the application of an incompressible Reynolds-averaged Navier –Stokessolver to several upwind cases from the NREL/NASA Ames wind tunnel tests. In connectionwith the NREL blind code comparison the present results showed the overall best agreementwith experimental measurements. Based on this, it is of great interest to demonstratethe quality that can be obtained in 3D CFD rotor computations. All six cases we presenthave 0° yaw angle and 3° tip pitch angle. All computations are performed as rotor-onlycomputations, excluding the tower and nacelle. In this article we compare computed resultsand measurements in the form of shaft torque, flap and edge moments, aerodynamiccoefficients and pressure distributions as a function of wind speed. The spanwise forcedistributions are compared with measurements for all wind speeds, along with the pressuredistributions at five spanwise positions. Finally, we show how 3D CFD computations canbe used to extract information about three-dimensional aerodynamic effects. Copyright 2002 John Wiley & Sons, Ltd.

Introduction

In the design process of new rotor blades the need for accurate aerodynamic predictions is very important.During the last couple of years a large effort has gone into developing CFD tools for prediction of windturbine flows. Previously, full Navier–Stokes simulations of wind turbine rotors have been performed byDuque,1 Xu and Sankar,2,3 Sørensen and Hansen4 and Sørensen and Michelsen.5 Additionally, a large numberof rotor simulations have been performed in the helicopter community. In the model development phase,validation against measurements is very important. Typically, only integrated loads are available from full-scale wind turbine measurements under atmospheric conditions. Additionally, full-scale measurements areoften contaminated by varying wind speed, changes in wind direction, etc. Detailed sectional informationin the form of pressure distributions has only been measured to a very limited degree.6 The NREL/NASAAmes wind tunnel test7 and the following NREL/NWTC aerodynamics blind comparison8 therefore offereda unique opportunity to assess and demonstrate the capability of modern CFD tools to predict rotor flows incomparison with other approaches. Herein all computations were performed without prior knowledge of themeasured results. The following is a presentation of the results computed using the EllipSys3D CFD code for

Ł Correspondence to: N. N. Sørensen, Risø National Laboratory, Wind Energy Department, PO Box 49, DK-4000 Roskilde,Denmark. E-mail: [email protected]/grant sponsor: Danish Energy Agency; Contract/grant number: ENS 1363/00-0007.

Received 13 November 2001Copyright 2002 John Wiley & Sons, Ltd. Revised 5 March 2002

Accepted 20 March 2002

152 N. N. Sørensen, J. A. Michelsen and S. Schreck

the blind comparison. Additionally, computations of a configuration consisting of a simplified representationof the wind tunnel are included to investigate the influence of tunnel blockage effects on the results.

Method

Navier–Stokes Solver

In the present work an incompressible Navier–Stokes solver is applied to predict the aerodynamics of theunsteady aerodynamics experiment Phase VI rotor from the National Renewable Energy Laboratory. Thetwo-bladed 10Ð058 m diameter Phase VI rotor geometry is based on the S809 aerofoil, and details about theblades can be found in Reference 9. For the cases considered in the present study, the rotor cone angle wasset at 0°. The blade pitch angle was set at 3°, which rotated the blade tip chordline 3° towards feather, relativeto the rotor plane, pointing the leading edge into the oncoming wind. In this investigation, only the upwindconfiguration will be examined, and the operational conditions for the cases computed can be found in Table I.The Reynolds number varies between 0Ð7 and 1Ð4 ð 106 at the root and between 1Ð0 and 1Ð1 ð 106 at theblade tip. The influence of the tower and nacelle on the rotor aerodynamics will be neglected, which is a fairapproximation for an upwind turbine. Besides removing the one-per-revolution periodic interference betweenthe tower and the individual rotor blades, this also greatly simplifies the geometrical complexity of the flowproblem. Additionally, assuming zero vertical shear in the incoming flow and zero yaw misalignment, theblades see the same inflow conditions irrespective of the azimuthal position of the rotor. These simplificationsresult in a problem where only the rotor needs to be modelled. As fluctuations from local flow separationson the blades may still lead to flow unsteadiness, both steady and unsteady computations are carried out. Forfurther details of the turbine properties, see Reference 10.

The computations submitted for the NREL aerodynamics blind comparison were performed assuming thatthe tunnel walls could be ignored, and only computations of a free rotor were carried out. Having comparedthe results with measurements, the question of whether inclusion of the tunnel could bring the predictions evencloser to measurements arose. A new series of computations was performed where a cylindrical approximationof the actual tunnel was included to determine the effect of tunnel blockage on the computed results. In thepresent work, only one of the blades is explicitly modelled in the computations. The remaining blade isaccounted for using periodic boundary conditions, exploiting the 180° symmetry of the two-bladed rotor.The information needed for this type of CFD computation is the geometry of the blade and the operationalparameters of the rotor (RPM, density, etc.). No empirical tuning is needed for a given rotor.

The in-house flow solver EllipSys3D is used in all computations presented in the following. Thecode was developed in co-operation between the Department of Mechanical Engineering at DTU and theDepartment of Wind Energy at Risø National Laboratory.11 – 13 The EllipSys3D code is a multiblock finitevolume discretization of the incompressible Reynolds-averaged Navier–Stokes (RANS) equations in generalcurvilinear co-ordinates. The code uses a collocated variable arrangement, and Rhie/Chow interpolation14 isused to avoid odd/even pressure decoupling. As the code solves the incompressible flow equations, no equationof state exists for the pressure, and the SIMPLE algorithm of Patankar and Spalding15 is used to enforce the

Table I. Operational conditions for the runs computed in the present work

Run RPM Windspeed

(m s�1)

Density(kg m�3)

Viscosityð105

(kg m�1 s�1)

S070000 71Ð9 7Ð0 1Ð246 1Ð769S100000 72Ð1 10Ð0 1Ð246 1Ð769S130000 72Ð1 13Ð0 1Ð227 1Ð781S150000 72Ð1 15Ð1 1Ð224 1Ð784S200000 72Ð0 20Ð1 1Ð221 1Ð786S250000 72Ð1 25Ð1 1Ð220 1Ð785

Copyright 2002 John Wiley & Sons, Ltd. Wind Energ. 2002; 5:151–169

Navier–Stokes Predictions 153

pressure/velocity coupling. The EllipSys3D code is parallelized with MPI for execution on distributed memorymachines, using a non-overlapping domain decomposition technique. For rotor computations a non-inertialreference frame attached to the rotor blades is used, and terms accounting for the Coriolis and centripetalforces are added to the equations. Polar velocities (vr , v� , vz) are used to allow simple treatment of periodicboundary conditions in the azimuthal direction.5,16 The solution is advanced in time using a second-orderiterative time-stepping (or dual time-stepping) method. In each global time step the equations are solved inan iterative manner, using underrelaxation. First, the momentum equations are used as a predictor to advancethe solution in time. At this point in the computation the flow field will not fulfil the continuity equation.The rewritten continuity equation (the so-called pressure correction equation) is used as a corrector to makethe predicted flow field satisfy the continuity constraint. This two-step procedure corresponds to a singlesubiteration, and the process is repeated until a convergent solution is obtained for the time step. Whena convergent solution is obtained, the variables are updated and the computation continues with the nexttime step.

For steady state computations the global time step is set to infinity and dual time stepping is not used.This corresponds to the use of local time stepping. To accelerate the overall algorithm, a three-level gridsequence is used in the steady state computations. The convective terms are discretized using a second-orderupwind scheme, implemented using the deferred correction approach first suggested by Khosla and Rubin.17

Central differences are used for the viscous terms. In each subiteration, only the normal terms are treatedfully implicitly, while the terms from non-orthogonality and the variable viscosity terms are treated explicitly.Thus, when the subiteration process is finished, all terms are evaluated at the new time level. The threemomentum equations are solved decoupled using a red/black Gauss–Seidel point solver. The solution of thePoisson system arising from the pressure correction equation is accelerated using a multigrid method.

In the present work the turbulence in the boundary layer is modelled by the k –ω SST model of Menter.18

The details of the model will not be given here. The model is chosen because of the very promising resultsfor 2D separated flows.19,20 The equations for the turbulence model are solved after the momentum andpressure correction equations in every subiteration/pseudo time step. In the present work, all computationsare performed assuming fully turbulent flow, excluding any laminar and transitional effects at the leadingedge region of the rotor.

Computational MeshAs previously discussed, two different configurations were computed in the present work. One is called thefree configuration, where the rotor is modelled without the presence of any external disturbances using a verylarge domain. The other is called the tunnel configuration, where a cylindrical approximation of the actualtunnel is included in the computations. In the tunnel configuration a cylindrical cross-section with an areaequal to the actual tunnel cross-section (24Ð4 m ð 36Ð6 m) is used, corresponding to a radius of 16Ð86 m. Thecylindrical approximation of the tunnel is used to avoid the need for sliding meshes, where one part of thecomputational mesh is moving with respect to another, which would be necessary if the actual tunnel wereto be modelled.

The mesh consists of three main components, shown in Figures 1 and 2. First, an inner five-block O–Otopology is used locally around the blade. This mesh component is identical for the two configurations. Second,an outer section is wrapped around the inner O–O section, containing three blocks for the free configurationand five blocks for the tunnel configuration. The inner O–O section and the outer section both cover only 90°

in the azimuthal direction. Finally, an additional mesh component is used to cover the remaining 90° of thecomputational domain. This section is simply generated by rotating the ‘periodic plane’ of the 90° section.In total, the mesh consists of 12 blocks of 643 cells or a total of 3Ð1 ð 106 cells for the free configurationand 16 blocks of 643 cells or a total of 4Ð2 ð 106 cells for the tunnel configuration.

The size of the inner O–O section is difficult to see in Figures 1 and 2, but the upstream and downstreamfaces are placed approximately 1 m away from the rotor plane. It has 64 cells in the direction normal to thesurface, 256 cells around the aerofoils and 64 cells in the spanwise direction. To facilitate the resolution of thetip of the blade, a 64 ð 64 block is placed at the tip. The total number of cells for the five-block inner O–O



Inlet

SymmetryPlanes

Figure 1. View through the outlet part of the mesh for the free configuration showing half of the domain (180° azimuth), withthe inner O–O section and the blade in the central part of the picture, the two 180° symmetry planes and the inlet/far-field

boundary

section is 1Ð3 ð 106. To resolve the boundary layer, the yC values at the wall are kept below 2 everywhereon the blade surface. Given the long computing times required for these 3D computations, the effect of gridsize on the solution accuracy cannot be readily evaluated at present. Instead, experience from previous 2Daerofoil computations and 3D rotor computations regarding the necessary number of mesh points was usedwhen designing the 3D mesh.

Boundary Conditions

In the following the boundary conditions are described for the two configurations, starting with the freeconfiguration and finishing with the tunnel configuration.

Free Configuration

For the free configuration, zero axial gradient is enforced at the outlet at the downstream end of the sphericaldomain where the flow leaves the domain. At the inner cylindrical face near the rotational axis, Euler/slipconditions are applied, while no-slip conditions are applied at the surface of the rotor blade. Fully implicitperiodic conditions are applied at the 180° cyclic boundaries. At the upstream part of the spherical domainthe undisturbed wind speed is specified. In the present computations, no attempt was made to include thetunnel walls and the corresponding blockage effects. Instead, a very large computational domain was usedand the rotor was computed in an undisturbed environment. With the present computational domain, which



Tunnel Wall

Symmetry Plane

Outlet

Symmetry Plane

Inlet

Figure 2. Overview of the tunnel mesh showing half of the domain (180° azimuth), with the inner O–O section and theblade in the central part of the picture, the two 180° symmetric planes, the inlet and outlet planes and part of the outer

tunnel wall. The figure shows every second mesh point only

placed the far-field boundary approximately 6 rotor diameters away from the rotor blades, no correction forthe presence of the rotor was necessary at the inlet boundary.

Tunnel Configuration

For the tunnel configuration a zero-axial-gradient condition is applied at the downstream boundary of thecylindrical domain where the flow leaves the domain. At the inner face near the rotational axis, Euler/slipconditions are applied, while no-slip conditions are applied at the surface of the rotor blade. Fully implicitperiodic conditions are applied at the 180° cyclic boundaries. At the upstream boundary of the cylindricaldomain the undisturbed wind speed is specified, while slip conditions are applied on the outer cylindrical partof the domain.

Computing Time

For all computations shown in the present article, the Risø IBM SP parallel computer was used. It is equippedwith eleven 375 MHz Power-3 SC Thin Nodes, each with two CPUs, and a 150 Mb s�1 switch connectionbetween the nodes. For the free configuration, both steady and time-accurate computations were performed.The steady state computations were continued for approximately 4500 iterations and took approximately 30 hper case on four CPUs. The unsteady computation used the steady state flow field as a starting conditionand carried out 830 time steps per revolution for 3Ð4 revolutions, which took approximately 40Ð8 h usingfour CPUs. For the tunnel configuration, only steady state computations were performed, as the previous freeconfiguration had shown very limited difference between the steady and time-accurate computations. The



steady state computations took approximately 40 h for 4500 iterations using four CPUs. Even though thelack of time-dependent behaviour may be caused by the relatively large time step used in the computations,limitation due to computing time prevents further time step refinement. Based on these facts, the applicationof time-accurate computations was not considered worthwhile for the tunnel configuration.

Results and DiscussionIn the following, the results of the Navier–Stokes simulations are compared with the results of theNREL/NASA Ames wind tunnel test. As stated earlier, the computations for the free configuration wereall completed before the release of the results from the measuring campaign. In contrast to this, the tunnelconfiguration computations were completed after the release of the measurements. In the following, integratedquantities (low-speed shaft torque, root flap and edge moments) will be presented first. Then the spanwisedistribution of normal and tangential forces will be compared to measurements, followed by a comparisonof computed and measured pressure distributions. All measurements except the pressure distributions areaveraged over several full revolutions, and š one standard deviations are shown where available to indicatethe variation over one revolution. The standard deviation of the measurements comprises several sources,including the disturbance from tower passage, dynamic loads, etc. The measured pressure distributionsrepresent averages of data acquired over the upper half of the rotor disc, where the influence of the tower isnegligible.

Integrated Loads

Looking first at the integrated loads, these are obtained from the computations by integrating the pressureand skin friction over the blade surface. In Figure 3 the low-speed shaft torque computed by the EllipSys3DCFD code is compared to measurements. Even though quantitative differences exist, the overall shape of thecomputed torque curve agrees well with the measured curve for both the free and the tunnel configuration. Theshaft torque at stall onset (10 m s�1) is overpredicted by 20%. This amount of overprediction is in the rangefound in previous rotor computations.21 At higher wind speeds under heavily stalled conditions the simulations

700

800

900

1000

1100

1200

1300

1400

1500

1600

1700

6 8 10 12 14 16 18 20 22 24 26

Low

Spe

ed S

haft

Tor

que

[Nm

]

Wind Speed [m/s]

Measured

Comp. Free

Comp. Tunnel

Figure 3. Comparison of measured and computed shaft torques for the NREL Phase VI rotor. For all measurements, šone standard deviations are shown to indicated the variation over one revolution



1000

1500

2000

2500

3000

3500

4000

4500

5000

6 8 10 12 14 16 18 20 22 24 26

Roo

t Fla

p M

omen

t [N

m]

Wind Speed [m/s]

Measured

Comp. Free

Comp. Tunnel

Figure 4. Comparison of measured and computed root flap moments. For the three highest wind speeds the deviations frommeasurements are less than the standard deviation

−600

−400

−200

0

200

400

600

800

1000

1200

1400

1600

6 8 10 12 14 16 18 20 22 24 26

Roo

t Edg

e M

omen

t [N

m]

Wind Speed [m/s]

MeasuredComp. Free

Comp. Tunnel

Figure 5. Comparison of measured and computed root edge moments. The large standard deviation for the measurementsis caused by the influence of gravity during one rotation

underpredict the shaft torque by approximately the same amount. The underprediction at high wind speedsdoes not agree with previous findings for the LM17.0 and LM19.1 blades, where Navier–Stokes solvers areknow to overpredict during stalled conditions.21 One reason for this difference may be that the present rotor isequipped with completely different aerofoil sections compared to the other rotors. A recent study has shownthat the aerofoil shape, and thereby the flow mechanisms controlling the stalling behaviour, may have a largeimpact on the quality of the CFD solution.22,23 When comparing computed and measured root flap moments,



0.4

0.5

0.6

0.7

0.8

0.9

1

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

CN

CN

CN

CN

CN

CN

S0700000

0.6

0.8

1

1.2

1.4

1.6

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

S1000000

0.4

0.8

1.2

1.6

2

2.4

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

S1300000

0.4

0.8

1.2

1.6

2

2.4

2.8

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

S1500000

0.4

0.8

1.2

1.6

2

2.4

2.8

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

S2000000

S2500000

0.4

0.8

1.2

1.6

2

2.4

2.8

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

r/R

(a)

(b)

(c)

(d)

(e)

(f)

Figure 6. Spanwise distribution of normal force coefficients for the six cases; for the measurements, š one standarddeviations are shown



0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

CT

S0700000

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

S1000000

CT

-0.1

0

0.1

0.2

0.3

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

S1300000

CT

-0.08-0.04

00.040.080.120.160.2

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

S1500000

CT

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

S2000000

CT

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

S2500000

CT

r/R

(a)

(b)

(c)

(d)

(e)

(f)

Figure 7. Spanwise distribution of tangential force coefficients for the six cases; for the measurements, š one standarddeviations are shown



good qualitative agreement is again found, as shown in Figure 4. For the three highest wind speeds (15Ð1,20Ð1 and 25Ð1 m s�1) the deviations from measured data are less than the standard deviations. For the twolowest wind speeds the computed values are approximately 16% overpredicted. Comparing the measured andcomputed root edge moments, good qualitative agreement is again found, as shown in Figure 5. Here thecomputed values are as much as 50% low compared to measurements. The large standard deviation for themeasurements is mainly caused by the influence of gravity during one rotation. The differences between theresults from the free and tunnel configurations are very small for all three integrated quantities and mostpronounced in all cases for the 10 m s�1 wind speed, where separated flow starts to cover the blade.

Blade ForcesTurning to the spanwise distribution of the normal and tangential force coefficients, good agreement isgenerally found, as shown in Figures 6 and 7. Generally, the computed sectional force coefficients fall withinone standard deviation of the measurements. The main exception is the S100000 run (10 m s�1), where largedeviations are seen on the inboard part of the rotor, especially in Figure 7.

Looking at the development of the tangential force components for increasing wind speed, the followingexplanation is suggested. When the wind speed reaches approximately 10 m s�1, the separation point issuddenly moved to the leading edge near the r/R D 0Ð47 section. As the wind speed increases further, thestalled area spreads, as seen by the widening of the dip of the tangential force coefficient in Figure 7. Inconnection with the computations there can be several reasons for not capturing this behaviour exactly. First,there is the generally accepted problem of accuracy of most turbulence models in highly separated flows.Second, the trends observed in the measurements may be connected to the presence of a laminar separation atthe leading edge, a phenomenon that will require the computations to include laminar-to-turbulent transition.Previously, we have suggested that the tunnel blockage effect may also influence this,24 and this is indeedseen in Figure 7. Even though a positive effect is seen on the tangential force component in Figure 7, adegradation is seen for the normal force in Figure 6. Close examination of the 10 m s�1 case has led us to

(a)

(b)

(c)

Figure 8. Limiting streamlines on the suction side of the blade. The cases shown are, from the top, 7, 10 and 20 m s�1 .The five vertical lines indicates the location of the 30%, 47%, 63%, 80% and 95% sections


grurichi

Hervorheben

grurichi

Hervorheben

grurichi

Hervorheben


-1.5

-1

-0.5

0

0.5

1

1.5

0 0.2 0.4 0.6 0.8 1

-Cp

X/Chord

r/R = 0.95(e)

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

3

0 0.2 0.4 0.6 0.8 1

-Cp

X/Chord

r/R = 0.30(a)

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

3

0 0.2 0.4 0.6 0.8 1

-Cp

X/Chord

r/R = 0.63(c)

-1.5

-1

-0.5

0

0.5

1

1.5

2

0 0.2 0.4 0.6 0.8 1

-Cp

X/Chord

r/R = 0.80(d)

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

3

3.5

0 0.2 0.4 0.6 0.8 1

-Cp

X/Chord

r/R = 0.47(b)

Figure 9. Pressure distributions for the 7 m s�1 case: circles, measurements; full curves, comp. free; dotted curves, comp.tunnel

believe that the tunnel blockage effect is not the main parameter. In fact, the tunnel blockage effect is verysmall. Instead, the fact that the flow is extremely unstable for this specific wind speed right at the onset ofmassive stall is the key issue. This fact makes the flow sensitive to the smallest disturbance, such as the smallchange in wind speed from the inclusion of the tunnel walls in the computation.

Pressure DistributionsIn the following, comparisons of measured and computed pressure distributions will be shown. In theexperiment, pressure distributions for five spanwise sections are measured at r/R D 0Ð30, 0Ð47, 0Ð63, 0Ð80 and



-2-10123456789

0 0.2 0.4 0.6 0.8 1

-Cp

X/Chord

r/R = 0.30(a)

-1

0

1

2

3

4

5

6

7

8

0 0.2 0.4 0.6 0.8 1

-Cp

X/Chord

r/R = 0.47(b)

-2

-1

0

1

2

3

4

5

6

7

0 0.2 0.4 0.6 0.8 1

-Cp

X/Chord

r/R = 0.63(c)

-2

-1

0

1

2

3

4

5

6

0 0.2 0.4 0.6 0.8 1

-Cp

X/Chord

r/R = 0.80(d)

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

3

0 0.2 0.4 0.6 0.8 1

-Cp

X/Chord

r/R = 0.95(e)

Figure 10. Pressure distributions for the 10 m s�1 case: circles, measurements; full curves, comp. free; dotted curves,comp. tunnel

0Ð95. In connection with the evaluation of the blind comparison a distinct deviation at the 95% section wasobserved for the highest wind speeds. In the blind comparison the EllipSys3D computations were performedusing an approximate tip shape, and this was suggested as a possible explanation of the deviations near thetip. For the computations of the tunnel configuration the actual tip geometry was used, as kindly providedby E. P. N Duque from Northern Arizona University. The definition used for the pressure coefficient in thefollowing is

Cp D P1 � P012 �C�W21 C �rω�2�



For the lowest computed wind speed of 7Ð0 m s�1, good agreement is found for all five spanwise sections,as shown in Figure 9. Referring to Figure 8, showing the limiting streamlines on the suction side of the blade,only the innermost station closest to the root experiences stalled flow conditions at this wind speed.

From the previous discussion of the integrated quantities and the spanwise force distributions it was observedthat the 10 m s�1 case is poorly predicted. Looking at Figure 10, it is obvious that the measurements show aleading edge separation at the r/R D 0Ð47 section, while the computations preserve a sharp suction peak. Acloser look at Figure 10 shows that the computation of the tunnel configuration has a slightly less pronounced

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

3

3.5

0 0.2 0.4 0.6 0.8 1

-Cp

X/Chord

r/R = 0.30(a)

-1.5

-1

-0.5

0

0.5

1

1.5

2

0 0.2 0.4 0.6 0.8 1

-Cp

X/Chord

r/R = 0.47(b)

-1

-0.5

0

0.5

1

1.5

2

0 0.2 0.4 0.6 0.8 1

-Cp

X/Chord

r/R = 0.63(c)

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

0 0.2 0.4 0.6 0.8 1

-Cp

X/Chord

r/R = 0.80(d)

-1

0

1

2

3

4

5

6

0 0.2 0.4 0.6 0.8 1

-Cp

X/Chord

r/R = 0.95(e)




-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

3

0 0.2 0.4 0.6 0.8 1

-Cp

X/Chord

r/R = 0.30(a)

-1.5

-1

-0.5

0

0.5

1

1.5

2

0 0.2 0.4 0.6 0.8 1

-Cp

X/Chord

r/R = 0.47(b)

-1.5

-1

-0.5

0

0.5

1

1.5

0 0.2 0.4 0.6 0.8 1

-Cp

X/Chord

r/R = 0.63(c)

-1.5

-1

-0.5

0

0.5

1

1.5

0 0.2 0.4 0.6 0.8 1

-Cp

X/Chord

r/R = 0.80(d)

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

0 0.2 0.4 0.6 0.8 1

-Cp

X/Chord

r/R = 0.95(e)


suction peak and therefore is slightly closer to the measured conditions. This is related to the previouslymentioned unstable flow conditions present near the r/R D 0Ð47 section. Here small spanwise shifts in theposition of the separation near the leading edge may cause significant changes to the pressure distribution, asshown in Figure 8.

For the higher wind speeds (15, 20 and 25 m s�1) the computed results show surprisingly good agreementwith the measured results, as shown in Figures 11–13. The stall behaviour of the S809 aerofoil is believedto be one explanation for the surprisingly good agreement for the high-wind-speed cases.



-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

0 0.2 0.4 0.6 0.8 1

-Cp

X/Chord

r/R = 0.30(a)

-1.5

-1

-0.5

0

0.5

1

1.5

2

0 0.2 0.4 0.6 0.8 1

-Cp

X/Chord

r/R = 0.47(b)

-1.5

-1

-0.5

0

0.5

1

1.5

0 0.2 0.4 0.6 0.8 1

-Cp

X/Chord

r/R = 0.63(c)

-1.5

-1

-0.5

0

0.5

1

1.5

0 0.2 0.4 0.6 0.8 1

-Cp

X/Chord

r/R = 0.80(d)

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0 0.2 0.4 0.6 0.8 1

-Cp

X/Chord

r/R = 0.95(e)


Recent investigation of the capability of the 2D Navier–Stokes solver EllipSys2D to model several aerofoilshas shown that the S809 belongs to a group of aerofoils where acceptable agreement between experiment andcomputation is found even at high angles of attack.22 Additionally, computations using the DES techniquehave indicated that resolving the vortex interaction in the wake at high angles of attack for the S809 aerofoilhas a limited effect on the computed loads compared to other investigated aerofoils.25 It is believed that theReynolds-averaged turbulence models perform well in 2D, and the limited dependence of the aerofoil loadson the 3D wake structure is mainly responsible for the quality of the rotor computations during heavily stalledconditions.



0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

0 10 20 30 40 50 60

Cl

AOA [deg]

r/R = 0.30

2D3D

(a)

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

0 10 20 30 40 50 60

AOA [deg]

r/R = 0.47

2D3D

Cl

(b)

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

0 10 20 30 40 50 60

AOA [deg]

Cl

(c) r/R = 0.63

2D3D

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

0 10 20 30 40 50 60

AOA [deg]

Cl

(d) r/R = 0.802D3D

r/R = 0.952D3D

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

0 10 20 30 40 50 60

AOA [deg]

Cl

(e)

Figure 14. Comparison of the computed lift for the five spanwise sections with 2D computed values

The deviation at the r/R D 0Ð95 section for the 20 m s�1 case is believed to be caused by an inaccuraterepresentation of the extremely complicated separated flow at the tip. The computations of the tunnelconfiguration have the correct tip geometry and show slightly better agreement at the tip. However, as seenfrom the surface streamlines in Figure 8, the flow in the tip region is extremely complicated and dominatedby three-dimensional effects from the tip vicinity.

3D EffectsTo investigate the changes to the 2D aerofoil characteristics when the aerofoils are used on rotating blades,lift and drag curves were extracted and compared to computed 2D curves. The method used to extract the



Cd

0 10 20 30 40 50 60

AOA [deg]

0

0.2

-0.2

0.4

0.6

0.8

1

1.2r/R = 0.95

2D3D

(e)

Cd

0 10 20 30 40 50 60

AOA [deg]

0

0.2

0.4

0.6

0.8

1

1.2r/R = 0.80

2D3D

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0 10 20 30 40 50 60

Cd

AOA [deg]

r/R = 0.30

2D3D

(a)

r/R = 0.632D3D

Cd

0 10 20 30 40 50 60

AOA [deg]

0

0.2

0.4

0.6

0.8

1

1.2(c) (d)

Cd

0 10 20 30 40 50 60

AOA [deg]

0

0.2

0.4

0.6

0.8

1

1.2r/R = 0.47

2D3D

(b)

Figure 15. Comparison of the computed drag for the five spanwise sections with 2D computed values

lift and drag is based on matching the stagnation point location between 2D and 3D CFD computations,both having been computed using the EllipSys code, as described in Reference 26. In Figures 14 and 15 thecomputed 3D lift and drag curves are compared with the 2D curves at the five spanwise sections. From thelift curves it is evident that there is large increase in lift for the inboard stations for high angles of attack.This is in good qualitative agreement with theory, where the increased lift is explained by radial pumpingof the flow in the separated area. When approaching the tip (r/R D 0Ð80 and 0Ð95), the flow is influenced bythe proximity of the blade tip, having the opposite effect on the lift. This is especially observed for the 95%section, where the lift is markedly reduced compared to 2D values. Next, looking at the drag, it is observedthat the increase in lift for the inboard stations is accompanied by increased drag also, as shown in Figure 15.


grurichi

Hervorheben


Conclusions

A series of computations of the NREL Phase VI rotor as tested in the NASA Ames wind tunnel duringupwind operation at 0° yaw and 3° tip pitch have been made. Generally, the computed results show goodqualitative and quantitative agreement with the measurements, the only exception being the 10 m s�1 windspeed case. The large deviation seen in the 10 s�1 case is believed to be connected to the very unstable flowbehaviour in this wind speed range. As the onset of massive flow separation on the blade is taking placefor wind speeds in the region of 10 m s�1, the prediction is very sensitive to very small variations. Changesin the wind speed, inclusion of laminar/turbulent transition, and the well-known problem of all turbulencemodels to capture the exact onset of stall will be extremely important in this connection.

It is also shown that the 3D CFD computations can be used to determine the 3D aerodynamic effects presenton wind turbine rotors. For the lowest wind speed, below onset of stall, the present CFD predictions accuratelypredict the low-speed shaft torque, while an overprediction of nearly 25% is observed at the onset of stall. Fordeep stall conditions an underprediction of 25% is observed. Additionally, the NREL/NWTC aerodynamicsblind comparison has shown that CFD computations are competitive with BEM-type computations for newand unknown rotors. Here the fact that CFD or Navier–Stokes computations do not rely on empirical inputhas proven to have distinct advantages. Additionally, the NREL/NASA Ames wind tunnel experiment hasproven to be extremely valuable in connection with code development and in the process of understandingthe flow physics of modern wind turbine rotors.

Acknowledgements

This work was carried out under a contract with the Danish Energy Agency, ENS 1363/00-0007, ‘Programfor research in aeroelasticity 2000–2001’. Computations were made possible by the use of the IBM RS/6000SP at the Risø central computing facility.

References1. Duque EPN, van Dam CP, Hughes SC. Navier–Stokes simulations of the NREL combined experiment phase II rotor.

AIAA Paper 99-0037, 1999.2. Xu G, Sankar LN. Computational study of horizontal axis wind turbines. AIAA Paper 99-0042, 1999.3. Xu G, Sankar LN. Effects of transition, turbulence and yaw on the performance of horizontal axis wind turbines.

AIAA Paper 2000-0048, 2000.4. Sørensen NN, Hansen MOL. Rotor performance predictions using a Navier–Stokes method. AIAA Paper 98-0025,

1998.5. Sørensen NN, Michelsen JA. Aerodynamic predictions for the unsteady aerodynamics experiment Phase-II rotor at

the National Renewable Energy Laboratory. AIAA Paper 2000-0037, 2000.6. Schepers JG, Brand AJ, Bruining A, Graham JMR, Hand MM, Infield DG, Madsen HA, Paynter RJH, Simms DA.

Final report of IEA Annex XIV: field rotor aerodynamics. Technical Report ECN-C-97-027, Netherlands EnergyResearch Foundation, 1997.

7. Fingersh L, Simms D, Hand M, Jager D, Cortrell J, Robinson M, Schreck S, Larwood S. Wind tunnel testing ofNREL’s unsteady aerodynamics experiment. AIAA 2001-0035, 2001.

8. Simms D, Schreck S, Hand M, Fingersh LJ. NREL unsteady aerodynamics experiment in the NASA-Ames windtunnel: a comparison of predictions to measurements. NREL/TP-500-29494, NREL, Golden, CO, 2001.

9. Giguere P, Selig MS. Design of a tapered and twisted blade for the NREL combined experiment rotor. NREL/SR-500-26173, NREL, Golden, CO, 1999.

10. Hand M, Simms D, Fingersh LJ, Jager D, Larwood S, Cotrell J, Schreck S. Unsteady aerodynamics experiment PhaseVI: wind tunnel test configurations and available data campaigns. NREL/TP-500-29955, NREL, Golden, CO, 2001.

11. Michelsen JA. Basis3D—a platform for development of multiblock PDE solvers. Technical Report AFM 92-05,Technical University of Denmark, Lyngby, 1992.

12. Michelsen JA. Block structured multigrid solution of 2D and 3D elliptic PDEs. Technical Report AFM 94-06, TechnicalUniversity of Denmark, Lyngby, 1994.

13. Sørensen NN. General purpose flow solver applied to flow over hills. Risø-R-827(EN), Risø National Laboratory,Roskilde, 1995.



14. Rhie CM. A numerical study of the flow past an isolated airfoil with separation. PhD Thesis, University of Illinois,Urbana-Champaign, IL, 1981.

15. Patankar SV, Spalding DB. A calculation procedure for heat, mass and momentum transfer in three-dimensionalparabolic flows. International Journal of Heat and Mass Transfer 1972; 15: 1787–1806.

16. Michelsen JA. General curvilinear transformation of the Navier–Stokes equations in a 3D polar rotating frame.Technical Report ET-AFM 98-01, Technical University of Denmark, Lyngby, 1998.

17. Khosla PK, Rubin SG. A diagonally dominant second-order accurate implicit scheme. Computers and Fluids 1974;2: 207–209.

18. Menter FR. Zonal two equation k–ω turbulence models for aerodynamic flows. AIAA Paper 93-2906, 1993.19. Wilcox DC. A half century historical review of the k–ω model. AIAA Paper 91-0615, 1991.20. Menter FR. Performance of popular turbulence models for attached and separated adverse pressure gradient flows.

AIAA Journal 1992; 30: 2066–2072.21. Chaviaropoulos PK, Nikolaou IG, Aggelis K, Sørensen NN, Montgomerie B, von Geyer G, Hansen MOL, Kang S,

Voutsinas S, Dyrmose SZ. Viscous and aeroelastic effects on wind turbine blades: the VISCEL project. EuropeanWind Energy Conference and Exhibition, Copenhagen, July 2001; 347–350.

22. Bertagnolio F, Sørensen NN, Johansen J, Fuglsang P. Wind turbine airfoil catalogue. Risø-R-1280(EN), Risø NationalLaboratory, Roskilde, 2001.

23. Bertagnolio F, Sørensen NN, Johansen J, Fuglsang P. Conclusion from the comparison of numerous 2D airfoilcomputations with experiments. AIAA Paper 2002-0034, 2002.

24. Sørensen NN, Michelsen JA, Schreck S. Detailed aerodynamic prediction of the NREL/NASA Ames wind tunneltests using CFD. European Wind Energy Conference and Exhibition, Copenhagen, July 2001; 48–53.

25. Johansen J, Sørensen NN, Michelsen JA, Schreck S. Detached-eddy simulation of flow around the S809 airfoil.European Wind Energy Conference and Exhibition, Copenhagen, July 2001; 414–417.

26. Sørensen NN. Evaluation of 3D effects from 3D CFD computations. IEA Joint Action. Aerodynamics of Wind Turbines.14th Symposium, Boulder, CO, December 2000; 11–22.


Navier–Stokes Predictions of the NREL Phase VI Rotor in the NASA Ames 80 ft ð 120 ft Wind Tunnel

Documents

wind energy wind energ

rotor aerodynamics

wind direction

wind speeds

oncoming wind

wind energy department

rotor ows

rotor plane