Numerical Simulation of the Aerodynamics of Horizontal Axis Wind Turbines under Yawed Flow...

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Chanin Tongchitpakdee1

e-mail: [email protected]

Sarun Benjanirat1


Lakshmi N. Sankar2


School of Aerospace Engineering, GeorgiaInstitute of Technology, Atlanta, GA 30332-0150

Numerical Simulationof the Aerodynamicsof Horizontal Axis Wind Turbinesunder Yawed Flow ConditionsThe aerodynamic performance of the National Renewable Energy Laboratory (NREL)Phase VI horizontal axis wind turbine (HAWT) under yawed flow conditions is studiedusing a three-dimensional unsteady viscous flow analysis. Simulations have been per-formed for upwind cases at several wind speeds and yaw angles. Results presentedinclude radial distribution of the normal and tangential forces, shaft torque, root flapmoment, and surface pressure distributions at selected radial locations. The results arecompared with the experimental data for the NREL Phase VI rotor. At low wind speeds��7 m/s� where the flow is fully attached, even an algebraic turbulence model basedsimulation gives good agreement with measurements. When the flow is massively sepa-rated (wind speed of 20 m/s or above), many of the computed quantities become insen-sitive to turbulence and transition model effects, and the calculations show overall agree-ment with experiments. When the flow is partially separated at wind speed above 15 m/s,encouraging results were obtained with a combination of the Spalart-Allmaras turbu-lence model and Eppler’s transition model only at high enough wind speeds.�DOI: 10.1115/1.2035705�

Keywords: Wind Turbine Aerodynamics, HAWT, Yawed Flow

1 IntroductionDuring the past few years, there has been increased interest in

the use of first-principles based computational approaches for theaerodynamic modeling of horizontal axis wind turbines �HAWT�.Since these approaches are based on the laws of conservation�mass, momentum, and energy�, they can capture much of thephysics in great detail. These approaches are particularly helpfulat high wind speeds, where appreciable regions of separation arepresent and the flow is unsteady. The ability to accurately modelthe airloads can greatly aid the designers in tailoring the aerody-namic and aeroelastic features of the configuration. An improvedunderstanding of the unsteady load environment will also helpwind turbine engineers to efficiently design the rotor structure tomeet the fatigue life requirements. First-principles based analysesare also valuable for developing active means �e.g., circulationcontrol�, and passive means �e.g., slotted airfoils and Gurneyflaps� of reducing unsteady blade loads, mitigating stall, and forefficient capture of energy.

Full Navier-Stokes simulations of HAWT configurations havebeen obtained using an overset grid approach by Duque �1�. In-compressible multiblock Navier-Stokes analyses have been usedby Sorensen and Hansen �2�, and by Sorensen and Michelsen �3�.Sorensen et al. �4� have reported excellent Navier-Stokes simula-tions for the National Renewable Energy Laboratory �NREL�Phase VI rotor tested at the NASA Ames Research Center. Theeffect of transition and turbulence models on the Navier-Stokespredictions has been studied by Xu and Sankar �5� and by Ben-janirat et al. �6�.

1Graduate Research Assistant, 270 Ferst Drive, Atlanta, GA 30332-0150, StudentMember AIAA.

2Regents Professor and Associate Chair �Academic�, 270 Ferst Drive, Atlanta, GA30332-0150, Associate Fellow AIAA.

Contributed by the Solar Energy Division of THE AMERICAN SOCIETY OF MECHANI-

CAL ENGINEERS. Manuscript received by the ASME Solar Division January 30, 2005;
final revision June 21, 2005. Associate Editor: P. Chaviaropoulos.
464 / Vol. 127, NOVEMBER 2005 Copyright ©

rom: http://solarenergyengineering.asmedigitalcollection.asme.org/ on 04/

The aerodynamics of the HAWT is more complex for yawedflow than for axial flow conditions as a consequence of the azi-muthal variation in the relative velocity between the blade sec-tions and the fluid. The skewed wake shed from the blade tipscauses unsteady, spatially nonuniform inflow through the rotor.Under certain conditions, blade-vortex interactions can occur.These factors may lead to flow separation, unsteady fluctuations inthe inflow through the rotor, and dynamic stall. Although thephysics behind these phenomena has been studied intensively�5–8�, attempts at modeling these effects have been limited due tothe computational complexity. Some recent noteworthy efforts inmodeling HAWTs under yawed flow conditions may be found inRefs. �7,8�.

2 MethodologyThe objective of the present research effort is to validate a

first-principles based approach for modeling HAWTs under yawedflow conditions using NREL Phase VI rotor data �9–12�. Thiscomputational effort is based on an unsteady viscous flow solverthat has been developed at Georgia Tech for modeling HAWTs.Prior applications of this approach under axial flow conditions aredocumented in Refs. �5,6�. Because the formulation has been ex-tensively documented in earlier publications, only a brief descrip-tion of the approach is given here.

In this approach, three-dimensional �3D� unsteady compressibleNavier-Stokes equations are solved on a computational grid sur-rounding a reference blade using a finite volume method. An im-plicit time-marching scheme is used to advance the viscous flowsolution on the grid surrounding the reference blade. The inviscidfluxes at the finite volume faces are computed using a third-orderaccurate upwind scheme. The viscous stresses at the cells arecomputed using a second order accurate approximation. Thesolver is third-order accurate in space and second order accuratein time.

The presence of other blades and the effects of the tip vortices
not captured by the computational grid are accounted for with an
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induced velocity flow field at the computational boundaries. Thetip vortex markers are initially generated and distributed azimuth-ally. The induced velocities are computed using Biot-Savart law.The induced velocity calculations require the tip vortex strength,computed as the peak bound circulation over the rotor. The calcu-lations also require a Lagrangean representation of the tip vortexstructure once it leaves the computational grid. The tip vortex isrepresented by a series of straight-line segments, on each of whichthe vortex strength is assumed to be constant. The end points ofthese segments �markers� and the strength of all segments arecomputed and updated at every 10 deg. increments of azimuth.

In the present work, all calculations are done on a C-O gridgenerated using an algebraic grid generator, shown in Fig. 1.There are 131 points in the C- or wraparound direction, 85 pointsin the radial direction including 56 radial stations on the rotorblade, and 55 points in the normal direction. The first point off thewall is placed at 0.0005 chords. The Reynolds number used in thisinvestigation varies between 1.25�106 and 1.29�106 at theblade tip. In our simulations, the largest y+ value at the wall oc-curs in the leading edge region, and approximately equals 10. They+ value, however, reduces to approximately 5 from the mid chordto the trailing edge. It is worthwhile to mention that normally y+

greater than 5 is not good with respect to the accuracy of mostturbulence models. The far field boundaries are placed approxi-mately six chords upstream and downstream the rotor blade. Thefar field boundary in spanwise direction is extended from theblade tip approximately one radius of the rotor.

Only the upwind configuration has been investigated to date.The effects of rotor tower and nacelle on the flow field have notbeen considered. All the calculations are done in a time-accuratemanner. At low wind speeds 14,400 time steps are needed perblade revolution, representing the rotational movement of the

Fig. 1 Overview of the me

blade by 1/40 deg. of azimuth every time step. At higher wind

Journal of Solar Energy Engineering


speeds, where unsteady effects are more dominant, a smaller timestep equivalent to a 1/80 degree azimuth is used. The time stepused in this sudy is in approximately 5�10−5 s, which is verysmall compared to the time constant for dynamic stall �c /�R� ofNREL case which is approximately 0.01 s. Therefore, the timestep chosen should be able to resolve dynamic stall.

Calculations are carried out for several revolutions, from animpulsive start of the rotor. Because the flow over the rotor underyawed flow conditions is inherently unsteady, only the informa-tion that is time-averaged over the last revolution is presented inall instances. Most of the calculations have been obtained usingthe Baldwin-Lomax turbulence model �13�. A limited number ofcalculations were done using Spalart-Allmaras model �14�. Theeffects of transition are modeled using Eppler’s transition criterion�15�. The reader is referred to Ref. �16� for further details of thismethodology. The second author has also done an independentevaluation of k-� model and a Detached-Eddy Simulation �DES�model for axial flow conditions �17�. The DES methodology ap-plies RANS near the solid surface and LES in the far field wherethe turbulence length scale is of the order of the grid size. How-ever, only selected k-� results are included in this study.

All computations in the present study were performed on adesktop computer with a single 2.40 GHz Intel Pentium IV pro-cessor, 256 MB of RAM, and a 60 GB of hard drive. For lowwind speed conditions, each revolution of the rotor �14,400 timesteps� took approximately 26 h of wall clock time. Calculationswere done for 2 to 3 rotor revolutions. The solutions from the finalrevolution were used in the following discussions.

As stated earlier, the solution is made of two parts: The imme-diate flow field over the rotor that is modeled using Navier-Stokesequations, and the far field wake that is analytically modeled for

used for the computations

several revolutions. When the solution is started, the effects of the

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7 m/s; Baldwin-Lomax turbulence model

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Fig. 2 Radial distribution of the normal force coefficient CN at
5 m/s; Baldwin-Lomax turbulence model
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Fig. 4 Radial distribution of the tangential force coefficient CT
at 5 m/s; Baldwin-Lomax turbulence model


Fig. 5 Radial distribution of the tangential force coefficient CT
at 7 m/s; Baldwin-Lomax turbulence model
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Fig. 6 Variation of the torque generated by the rotor as a func-tion of yaw angle; Baldwin-Lomax turbulence model

Fig. 7 Variation of the root flap moment as a function of yaw
angle; Baldwin-Lomax turbulence model
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Fig. 8 Pressure distribution of the 5 m/s and 30 deg yawcase; Baldwin-Lomax turbulence model



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Fig. 9 Pressure distribution of the 7 m/s and 30 deg yawcase; Baldwin-Lomax turbulence model



Fig. 10 Radial distribution of the normal force coefficient CN at20 and 25 m/s „zero yaw…

Fig. 11 Radial distribution of the tangential force coefficientC at 20 and 25 m/s „zero yaw…
T
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far field vortex structure are already accounted for in the calcula-tion. Thus only 2 to 3 revolutions are needed to establish the nearwake behind the blade that is captured by the Navier-Stokesanalysis, and to adjust the time-dependent strength of the tip vor-tex filaments. For further details of this procedure, the reader isreferred to the Ph D dissertation of Xu �16�.

3 Results and DiscussionCalculations have been obtained for the NREL Phase VI rotor

at four wind speeds �5, 7, 10, and 15 m/s�; at five yaw angles �0,10, 30, 45, and 60 deg.�. As stated earlier, an excellent experimen-tal database is available for this rotor, and has been used to cali-brate a variety of solution techniques �9–12�. The assessment ofthe present method was done by comparing the predictions withthe following measurements: �a� Radial variation of the normalforce coefficient CN and tangential force coefficient CT; �b� varia-tion of time-averaged torque generated by the rotor as a functionof yaw angle and wind speed; �c� time-averaged root flap momentvariation as a function of wind speed and yaw angle; �d� surfacepressure distributions at selected radial sections.

Because the flow over a rotor in yaw is inherently unsteady, theaerodynamic loads fluctuate about time-averaged �mean� values.The experimental database contains both unsteady �raw� data andtime averaged data. A large body of unsteady data was generatedas part of this study for four wind speeds and five yaw conditions.For brevity, comparisons with only the time averaged data arepresented here.

Fig. 12 Prediction of shaft torque with various turbulencemodels

Fig. 13 Prediction of root flap moment with various turbulence
case; k-� turbulence model models
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Fig. 14 Pressure distribution of the 25 m/s and zero yaw



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3.1 Low Wind Speed Attached Flow Conditions. We firstpresent results at low wind speeds of 5 and 7 m/s for yaw anglesup to 60 deg. At these conditions, a visualization of the computedflow indicates that the flow is well-behaved and attached overmuch of the rotor. Under these conditions, on the present grid andthe algebraic turbulence model, one can expect the results to be inreasonable agreement with measurements. This indeed turns out tobe the case.

Figures 2 and 3 show the radial distribution of the pressureforce normal to the chord at 5 and 7 m/s, respectively. A reason-able agreement with measurements is observed. Figures 4 and 5

Fig. 15 Radial distribution of the normal force coefficient CN at15 m/s „30 and 45 deg yaw…

Fig. 16 Variation of the torque generated by the rotor as a
function of yaw angle; at 15 m/s


show the corresponding tangential forces at 5 and 7 m/s, respec-tively. It should be noted that the tangential forces are quite sen-sitive to the pressure distribution in the leading edge stagnationregion, and trailing edge recompression region. Since the experi-ments had only a few pressure taps in these regions, one cannotexpect the measured CT values to be as accurate as the CN values.The qualitative agreement between the measurements and the pre-dictions is reasonable when this uncertainty in the measurementsof CT is factored in. The prediction of transition influences theprediction of skin friction drag, and can also affect the tangential

Fig. 17 Variation of the root flap moment as a function of yawangle; at 15 m/s

10 m/s „10 and 30 deg yaw…
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force at these low wind speeds.Figure 6 shows the variation of shaft torque with yaw angle at

these wind speeds. Whereas the trend is correctly predicted, thecomputed torque shows approximately 30% discrepancy at thelower wind speed of 5 m/s. The shaft torque at these low windspeeds is dominated by the radial distribution of the tangentialforces, which could not be predicted well. At the higher windspeed of 7 m/s, the discrepancy between prediction and measure-ments is within 10%.

Figure 7 shows the root flap moment as a function of yawangle. This quantity is dominated by the normal force effects. Theroot flap moment is weighted with the radius and therefore therelatively large errors at the inboard section contribute relativelysmall. Good agreement with experiment is observed. Figures 8and 9 show representative surface pressure distributions at se-lected radial locations and yaw angles, at wind speed 5 and 7 m/s,respectively. Good agreement is observed except in the inboardregions where the use of a compressible flow solver at extremelylow wind speeds creates spurious spikes in the vicinity of theleading edge stagnation point.

3.2 High Wind Speed Fully Separated Flow Conditions.We next look at another extreme case, where the wind velocity ishigh enough �20 and 25 m/s� to cause flow separation over theentire upper surface. At this writing, results are available only forzero yaw. Because the flow was fully separated, some of thesesimulations were repeated using more advanced turbulence mod-els �one equation S-A model, and a two-equation k-� model�. Thek-� results were computed using a companion H-O grid basedsolver with comparable number of grid points �17�.

Figures 10 and 11 show the radial distribution of the normaland tangential forces at zero yaw condition using various turbu-lence models. The normal force was again in reasonable agree-ment. Above 20 m/s, because the flow is massively separated,there is a very large pressure drag and the tangential force isnegative over much of the rotor. Under high wind conditions, thetorque generation is influenced more by the in-plane componentof the lift force. Only the S-A model based predictions were inreasonable agreement �Fig. 12� at these wind speeds. The root flapmoment �Fig. 13� is CN times r /R integrated over the blade ra-dius. This quantity is sensitive to small variations in the CN valuesnear the tip shown on Fig. 10, because of the large moment arm.Only the k-� model predicted reasonable agreement with measure-ments. Based on Figs. 12 and 13, it may be concluded that none ofthe models considered here �B-L, S-A, k-�� gave uniformly goodagreement for the torque and the root flap bending moment atthese high wind speeds.

The pressure distributions at 25 m/s shown in Fig. 14 are simi-lar in quality to Figs. 8 and 9. The agreement is reasonable exceptat the inboard stations where the present approach does not cap-ture the pressure plateau seen in experiments, caused by flowseparation.

3.3 Transitional Partially Separated Flow Conditions. Wenext look at the flow conditions �wind speed of 15 m/s�, wherethe flow over the rotor is partially separated. Calculations havebeen obtained at five yaw angles: 0, 10, 30, 45, and 60 deg. Onlyrepresentative results are shown due to manuscript length restric-tions. In this regime, the flow is sensitive to both the turbulencemodel and the transition model. In the present study, Eppler’stransition model was used �16�. It is seen that the normal forces�Fig. 15�, shaft torque �Fig. 16�, and root flap moment �Fig. 17�are all well predicted with the S-A turbulence model-Eppler’stransition model combination. The surface pressure distributionswere also better predicted with the S-A and Eppler’s model. TheBaldwin-Lomax model based simulations tend to overpredict boththe normal and the tangential forces.

In the speed regime between 7 and 15 m/s �e.g., at 10 m/s�,none of the combinations �transition model, turbulence model�
gave acceptable results for CT and for torque, although CN distri-
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butions and root flap moments were reasonable �see Figs. 18–21�.In this regime, transition plays a critical role in where flow sepa-ration occurs. Separation prediction affects the pressure distribu-tion, particularly in the leading edge suction region. The tangentialforce CT is sensitive to these effects and could not be predictedwell.

3.4 Variation of Power as a Function of Wind Speed. Fi-nally, we look at the power generated by rotor in Fig. 22. This isthe same information presented in Figs. 6, 16, and 20, and wasreplotted as a function of wind speed. At low wind speed condi-

Fig. 19 Radial distribution of the tangential force coefficientCT at 10 m/s „10 and 30 deg yaw…

Fig. 20 Variation of the torque generated by the rotor as a
function of yaw angle; at 10 m/s


Fig. 22 Comparison of computed and measured rotor power

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tions �5 and 7 m/s�, where the flow remains attached over muchof the rotor, the computed results show good agreement with theexperiments. The agreement is observed in the high yawed flowconditions as well. At wind speeds greater than 10 m/s and at lowyaw angles the present study does not properly model the partiallyseparated flow over the rotor; the predictions exhibit some dis-crepancies. At high yaw angles �45 and 60 deg. yaw�, where thereis less flow separation over the upper surface, the computed re-sults are again in reasonable agreement even at high wind speeds.

4 ConclusionsThe aerodynamics of the NREL Phase VI rotor under yawed

flow conditions has been analyzed at four wind speeds and fouryaw angles. The conditions chosen for detailed study range fromfully attached flow to massively separated flow. Calculations haveobtained done using a time-accurate viscous flow solver, and time-averaged quantities are extracted for comparisons with experi-ments. The following conclusions are drawn:

1. At low wind speeds ��7 m/s� where the flow is fully at-tached, even a Baldwin-Lomax model based simulationgives good agreement with measurements.

2. When the flow is massively separated �20 m/s or above�,many of the computed quantities become insensitive to tur-bulence model effects, and the calculations show overallagreement with experiments.

3. When the flow is partially separated, encouraging resultswith a combination of S-A turbulence model and Eppler’stransition model were obtained only at high enough windspeeds �above 15 m/s�. Between 7 and 15 m/s, more so-phisticated turbulence models and transition models may benecessary. A fine grid for accurate resolution of the separa-tion may also be necessary.

At this writing, the present authors are doing studies to improvethe correlations. Grid sensitivity studies and advanced turbulencemodeling �Detached-Eddy Simulation� are both being investi-gated.

AcknowledgmentsThis work is supported by the National Renewable Energy

Laboratory under Contract No. XCX-2-32227-02. The authors aregrateful to Dr. Scott Schreck, the technical monitor, for kindlyproviding experimental data and for many helpful comments.

NomenclatureCN � Normal force coefficient

Fig. 21 Variation of the root flap moment as a function of yawangle; at 10 m/s

Cp � Pressure coefficient



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CT � Tangential force coefficientc � Rotor chord �m�R � Rotor radius �m�r � Radial position from hub �m�X � Chordwise position �m�

y+ � Nondimensional distance of the first grid pointoff the blade surface

� � Rotor rotation rate �rad/s�

References�1� Duque, E. P. N., van Dam, C. P., and Hughes, S., 1999, “Navier-Stokes Simu-

lations of the NREL Combined Experiment Phase II Rotor,” AIAA Pap. 99-0037.

�2� Sorensen, N. N., and Hansen, M. O. L., “1998, Rotor Performance Predictionsusing a Navier-Stokes Method,” AIAA Pap. 98-0025.

�3� Sorensen, N. N., and Michelsen, J. A., 2000, “Aerodynamic Predictions for theUnsteady Aerodynamics Experiment Phase-II Rotor at the National RenewableEnergy Laboratory,” AIAA Pap. 2000-0037.

�4� Sorensen, N. N., Michelsen, J. A., and Schreck, S., 2002, “Prediction of theNREL/NASA Ames Wind Tunnel Test,” AIAA Pap. 2002-0031.

�5� Xu, G., and Sankar, L. N., 2000, “Effects of Transition, Turbulence and Yawon the Performance of Horizontal Axis Wind Turbines,” AIAA Pap. 2000-0048.

�6� Benjanirat, S., Sankar, L. N., and Xu, G., 2003, “Evaluation of TurbulenceModels for the Prediction of Wind Turbine Aerodynamics,” AIAA Pap. 2003-
0517.
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�7� Duque, E. P. N., Burklund, M. D., and Johnson, W., 2003, “Navier-Stokes andComprehensive Analysis Performance Predictions of the NREL Phase VI Ex-periment,” AIAA Pap. 2003-0355.

�8� Madsen, H. A., Sorensen, N. N., and Schreck, S., 2003, “Yaw AerodynamicsAnalyzed with Three Codes in Comparison with Experiment,” AIAA Pap.2003-0519.

�9� Hand, M. M., Simms, D. A., Fingersh, L. J., Jager, D. W., Cotrell, J. R.,Schreck, S., and Larwood, S. M., 2001, “Unsteady Aerodynamics ExperimentPhase VI: Wind Tunnel Test Configurations and Available Data Campaigns,”National Renewable Energy Laboratory, NREL/TP-500-29955, Golden, CO.

�10� Simms, D. A., Schreck, S., Hand, M. M., and Fingersh, L. J, 2001, “NRELUnsteady Aerodynamics Experiment in the NASA-Ames Wind Tunnel: AComparison of Predictions to Measurements,” NICH Report No. TP-500-29494.

�11� Fingersh, L. J., Simms, D. A., Hand, M. M., Jager, D. W., Cotrell, J. R.,Robinson, M., Schreck, S. and Larwood, S. M., 2001, “Wind Tunnel Testing ofNREL’s Unsteady Aerodynamics Experiment,” AIAA Pap. 2001-0035.

�12� Giguere, P., and Selig, M., 1999, “Design of a Tapered and Twisted Blade forthe NREL Combined Experiment Rotor,” National Renewable Energy Labo-ratory, NREL/SR-500-26173, Golden, CO.

�13� Baldwin, B. S., and Lomax, H., 1978, “Thin Layer Approximation and Alge-braic Model for Separated Turbulent Flows,” AIAA Pap. 78-257.

�14� Spalart, P. R., and Allmaras, S. R., 1992, “A One-Equation Turbulence Modelfor Aerodynamic Flows,” AIAA Pap. 92-0439.

�15� Eppler, R., 1990, Airfoil Design and Data, Springer-Verlag, New York, p. 562.�16� Xu, G., 2001, “Computational Studies of Horizontal Axis Wind Turbines,”

Ph.D. Dissertation, School of Aerospace Engineering, Georgia Institute ofTechnology, Atlanta, GA.

�17� Benjanirat, S., Ph.D. Dissertation, School of Aerospace Engineering, Georgia
Institute of Technology, Atlanta, GA �under preparation�.


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