COUPLED CFD/CSD METHOD FOR WIND TURBINEScongress.cimne.com/iacm-eccomas2014/admin/files/file...NREL Phase VI wind turbine (including 2 blades, hub, nacelle and tower), using ICEM-HexaTMof

11th World Congress on Computational Mechanics (WCCM XI)5th European Conference on Computational Mechanics (ECCM V)

6th European Conference on Computational Fluid Dynamics (ECFD VI)E. Oñate, J. Oliver and A. Huerta (Eds)

COUPLED CFD/CSD METHOD FOR WIND TURBINES

Marina Carrion∗, Rene Steijl∗, George N. Barakos∗, Sugoi Gomez-Iradi† andXabier Munduate†

∗ Computational Fluid Dynamics Laboratory, School of Engineering, University of Liverpool,Harrison Hughes Building, Liverpool, L69 3GH, U.K.

e-mail: [email protected] - Web page: http://www.liv.ac.uk/engdept

†National Renewable Energy Centre of Spain (CENER)Ciudad de la Innovación 7, 31621 Sarriguren (Navarra), Spaine-mail: [email protected] - Web page: http://www.cener.com

Key words: Aeroelasticity, CFD-CSD coupling, NREL Phase VI wind turbine

Abstract. This paper presents an aeroelastic analysis of the NREL Phase VI windturbine, using the HMB2 solver of Liverpool University, coupled with a CSD method.Flapping modes were found to be the most dominant, due to the structural properties ofthis blade. The employed method enabled the study of the effect of the blade flapping onthe loads, in conjunction with the effect of tower, for a low and a high speed case.

1 INTRODUCTION

To maximise the amount of produced energy, the diameter of wind turbines have beenincreasing during the last 25 years, reaching values of more than 160m. When analysingwind turbines of that size, aeroelasticity plays an important role, since the blades areless stiff and can undergo large deformations, changing their aerodynamic performance.As Hansen et al. explain in their review paper [1], wind turbines suffer from aeroelasticinstabilities, such as edgewise blade vibration, usually encountered in parked rotors, andflutter, due to the interplay between unsteady aerodynamic loads and the wind turbinestructure. In order to study the interaction between the flow and the structure of the windturbine, aeroelastic methods have been developed over the years, where the aerodynamicand structural information is exchanged.

To obtain the aerodynamic loads, BEM-based methods are popular in the literature,since they do not require large computational effort. However, they have limitations whensimulating more complex flows, which are three-dimensional and unsteady. That is whydevelopment and application of CFD-CSD coupling methods for wind turbine analysishave been on the increase. With this regard, Bazilevs et al. [2] used a CFD solver tocompute the Navier-Stokes equations and a CSD solver based on rotation-free thin shell

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Marina Carrion, Rene Steijl, George N. Barakos, Sugoi Gomez-Iradi and Xabier Munduate

formulation for the structural analysis of composite blades, and the information betweensolvers was exchanged at each time-step. The 5MW RWT (Reference Wind Turbine)was employed, where only one blade was considered, imposing spatial periodicity, and amaximum deflection in flapping of 10%R and in torsion of 2 deg. were reported. Yu etal. [3] used an incompressible, unstructured Navier-Stokes CFD solver loosely coupledwith a CSD FEM solver (using on non-linear flap-lag-torsion beam theory) to obtain theblade deformations of the 5MW RWT case at rated wind speed. For static cases, theexchange of information between the CFD and CSD solvers was done at the end of theCFD simulation, once the loads were converged. For unsteady cases, the exchange wasdone once per revolution, under the assumption of load periodicity. For the static case,a torsion at the tip of 3.1 deg. (nose-down) was obtained and deflections in lead-lag andflapwise of 10%R and 7.5%R, respectively, leading to a significant reduction in thrust andtorque. The unsteady computation considering the full machine showed similar averagedvalues to the steady-state results and a reduction in the tower clearance of 40% for theelastic blades was observed, along with a substantial reduction on the loads. Finally, Guoet al. [4] presented a CFD-CSD coupled method, where the N-S equations were solvedalong with the modal amplitudes at each solution update, using a predictor-correctorscheme. The interpolation from structural to aerodynamic nodes was performed with alinear interpolation scheme, since the blade was simplified as a one-dimensional beam.For validation of the method, they used the blades of the NH1500 wind turbine of 40.5mradius and obtained flapwise deformations with a frequency close to its natural frequencyand edgewise deformations at frequency close to the rotational one.

To the best of the author’s knowledge, in the CFD-CSD methods in the literatureapplied to wind turbines the exchange of aerodynamic/structural information is fully de-coupled or loosely coupled. Likewise, the role of aeroelasticity has not been fully assessedfor the NREL Phase VI wind turbine. It is therefore the objective of this paper to presenta tightly coupled CFD-CSD method and its application to this wind turbine model.

2 NUMERICAL METHOD

2.1 CFD Solver

The Helicopter Multi-Block (HMB2) code [5], developed at Liverpool, is used for thepresent work. HMB2 solves the Navier-Stokes equations in integral form using the arbi-trary Lagrangian Eulerian formulation for time-dependent domains with moving bound-aries:

d

dt

∫V (t)

w⃗dV +

∫∂V (t)

(F⃗i (w⃗)− F⃗v (w⃗)

)n⃗dS = S⃗ (1)

where V (t) is the time dependent control volume, ∂V (t) its boundary, w⃗ is the vector

of conserved variables [ρ, ρu, ρv, ρw, ρE]T . F⃗i and F⃗v are the inviscid and viscous fluxes,including the effects of the mesh movement.

2


The Navier-Stokes equation are discretised using a cell-centred finite volume approachon a multi-block grid, leading to the following equation:

∂

∂t(wi,j,kVi,j,k) = −Ri,j,k (wi,j,k) (2)

where w represents the cell variables and R the residuals. i, j and k are the cell indicesand Vi,j,k is the cell volume. To account for low-speed flows, Low-Mach Roe’s [6] is used forfor the discretisation of the convective terms and MUSCL variable extrapolation is usedfor higher order accuracy. The linearised system is solved using the generalised conjugategradient method with a block incomplete lower-upper pre-conditioner. The solver hasbeen used for several types of flows, including wind turbines [7, 8].

2.2 CSD Solver

2.2.1 Structural model

NASTRAN [9] is used for calculating the eigenmode shapes and frequencies of theNREL Phase VI blade [10], which is modelled as a beam. 22 non-linear elements ofCBEAM type are used, placed along the quarter-chord line of the blade, as shown inFigure 1. The main structural properties needed for this analysis are the distributionsof the sectional area, the chordwise and flapwise area moments of inertia, the torsionalconstant and the linear mass distribution along the span. All structural properties arelinearly interpolated between the ends of each beam element. Rigid bar elements (RBAR)without any structural properties are also used for interpolating the beam model defor-mation to the blade surface, which is then used for deforming the CFD fluid grid. TheNASTRAN model was modified in order to match the first flapwise and edgewise naturalfrequencies, and then the centrifugal forces were applied, employing a non-linear staticanalysis (SOL 106).

0.30R 0.466R 0.633R 0.80R 0.95R

1R = 5.03m

RBAR CBEAM

Figure 1: Structural model for the blades, including 22 CBEAM elements with structural propertiesand RBAR rigid elements. The the position of the pressure transducers are indicated in dashed lines.

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The natural frequencies were obtained using modal analysis in NASTRAN and, amongthe ten first harmonics, no torsional modes were found. Figure 2 shows the flapping andedgewise modes.

r/R

z/R

0 0.2 0.4 0.6 0.8 1-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4RigidMode 1: 7.34HzMode 2: 20.13HzMode 3: 39.65HzMode 4: 59.34HzMode 5: 76.73Hz

r/Ry/

R0 0.2 0.4 0.6 0.8 1

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4RigidMode 1: 8.79HzMode 2: 26.03HzMode 3: 47.47HzMode 4: 64.39HzMode 5: 81.91Hz

(a) Flapping modes. (b) Edgewise modes.

Figure 2: Mode shapes in flap and edgewise vibration, normalised with the blade radius.

2.3 Dynamic CFD-CSD method

A modal approach is followed in the CFD-CSD coupled method. For this, the bladeshape (ϕ) is expressed as a sum of eigenvectors (ϕi), which represent the blade displace-ments for each eigen-mode, multiplied by a modal amplitude αi. The differential equationfor the modal amplitude is solved at each time step:

∂2αi∂t2

+ 2ζiωi∂αi∂t

+ ω2i αi = fϕi, (3)

where f represents external forces, ωi the ith eigen-frequencies and ζi the ith dampingcoefficients. For stability purposes, the analysis is started with strong damping of ζi = 0.7and once the blade reaches a level of deformation of 80-90%, usually after a half of arevolution, the damping is brought back to smaller values (e.g. ζi = 0.03). At each pseudo-time step of the employed dual time-step method, the modal amplitudes are computedsolving Equation 3, the CFD grid is deformed and the flow field updated solving the N-Sequations. At the end of each time step, the blade loads are extracted and re-applied tothe system. This process is performed repeatedly until the end of the computation.

2.4 Mesh deformation

The mesh deformation in HMB2 [11] is performed in three stages. The blade surfaceis first deformed using the Constant Volume Tetrahedron (CVT) method, which projectseach fluid node (F) to the nearest structural triangular element (S1, S2, S3), and moves itlinearly with the element, as shown in the shaded region of Figure 3. The vertex positions

4


are updated via spring analogy (SAM), which consists of adding springs along the sidesand the diagonals of each surface of the mesh, which allows to preserve the quality of themesh. Finally, the full mesh is generated via Transfinite Interpolation (TFI). For this, theblock faces are interpolated from the edge deformations, which in turn are used for theinterpolation of the full blocks deformations.

Figure 3: Projection of the fluid grid on the structural model through Constant Volume Tetrahedron(CVT). (a) Blade shape, (b) Blade structural model, (c) Block boundaries of the fluid grid, (d,e) Springsfor the Spring Analogy (SAM) in conctact and not in contact with the blade, respectively.

3 SIMULATIONS SETUP

A multi-block structured topology was employed for the grid generation around theNREL Phase VI wind turbine (including 2 blades, hub, nacelle and tower), using ICEM-HexaTMof ANSYS. Around the blades, a C-topology was employed, which leads to goodboundary layer resolution (Figure 4 (a)). To account for the rotation of the rotor, whilethe nacelle and the tower are fixed, one sliding plane was employed, as shown in Figures4 (b). The mesh had a total of 18 million cells and 128 CPU cores were employed.

A number of rotor revolutions with rigid blades was first performed and the aeroelasticmethod was activated once a quasi-periodic behaviour was achieved. Unsteady steps of0.25 degrees were used and wind speed cases of 7 and 20m/s were studied (keeping therotational speed at 72rpm), corresponding to tip speed ratios of 5.4 and 1.88, respectively,at 0 degrees of yaw and 3 degrees of pitch. For the aeroelastic computation, only the bladeswere allowed to deform, while keeping the hub, nacelle and tower rigid. The first fourharmonics presented in Figure 2 were included in the structural model, corresponding tothe first and second flapping and edgewise modes. Regarding turbulence modeling, andsince the flow at 7m/s is attached along the blades, the k-ω SST model [12] was employed.Conversely, the higher wind speed case was reported in the literature to suffer from stallover the blade, hence, the Scale-Adaptative Simulation (SAS) method [13] was employed.

5


(a) Multi-block grid around a blade section. (b) Computational domain.

Figure 4: Employed blocking topology and grid for the NREL Phase VI wind turbine, including bound-ary conditions and the extend of the domain. SP represents the location of the sliding mesh plane.

4 RESULTS AND DISCUSSION

4.1 Effect of the wind speed on the type of flow

Figure 5 shows iso-surfaces of λ2-criterion [14], at an instance when the reference bladeis at 45 degrees of azimuth, for both wind speed cases. The interaction of the wakegenerated by the rotor and the Kárman vortex street generated by the cylindrical towercan be clearly identified.

(a) 7m/s (λ = 5.04). (b) 20m/s (λ = 1.88).

Figure 5: Visualisation of the rotor and tower wakes with iso-surfaces of λ2-criterion (λ2 = −0.25) forwind speeds of (a) 7m/s and (b) 20m/s. The reference blade is positioned at 45 deg. of azimuth (counterclock-wise rotation WT).

At 7m/s the flow is attached and the tip vortex is captured and preserved up to 2 radiidownstream the rotor plane, where the grid starts to be coarser. On the other hand, at

6


20m/s the vortical structures immediately behind the blades suggest separated flow onthe blade. Due to the large step of the wake espiral at the 20m/s case, the wake reachesthe coarse portion of the mesh relatively early and begins to dissipate prematurely.

Figure 6 shows FFTs of the sectional thrust at three blade stations. More frequencycontent is observed in the 20m/s wind speed case than at 7m/s. This is due to the presenceof stall almost everywhere on the blade for this high wind speed case. In addition, thereis a peak very close to the first flapping mode, which could trigger flutter.

f (Hz)

A (

T)

0 5 10 15 20 25 300

0.5

1

1.5

2

HarmonicsNatural freq.r=30%Rr=63.3%Rr=95%R

f (Hz)

A (

T)

0 5 10 15 20 25 300

4

8

12

16

20

HarmonicsNatural freq.r=30%Rr=63.3%Rr=95%R

(a) 7m/s. (b) 20m/s.

Figure 6: FFTs of sectional thrust at three blade stations, for wind speeds of (a) 7m/s and (b) 20m/s.The harmonics correspond to multiples of the blade passing frequency fn = nf1 (f1 =2.4Hz). The naturalfrequencies are: fn1 = 7.34, fn2 = 8.79, fn3 = 20.13, fn4 = 26.03.

4.2 Study of the blade deformations

Figures 7 (a) and (d) show the flapping motion of the leading edge of the blade tipduring the fifth aeroelastic revolution. With the employed sign convention, negative δindicates that the blade deflects towards the tower and blade 2 has been plotted with anazimuthal shift of 180 degrees, for easier comparison. As can be observed in Figure 7 (a),the mean deflection at 7m/s is 1.73% of the blade’s maximum aerodynamic chord (13mm)towards the tower, with maximum oscillations of approximately +/− 5.2% with respectto the mean value. A mean deflection of 4%c (29mm or 0.59%R) is observed in the 20m/scase (Figure 7 (d)) and oscillates around that mean value with maximum amplitudes of+/−30%. The maximum amplitudes are present after the blades have passed in front ofthe tower (Ψ = 0deg. and Ψ = 180deg. for blades 2 and 1, respectively), with a delay of20 degrees at 7m/s wind speed and 40 degrees at 20m/s.

The derivatives of the flapping are shown in Figures 7 (b) and (e), in chords per second.Negative values add extra velocity to the axial component, while positive values reducethe axial velocity. The maximum increase/decrease of velocities is of 0.02 and 0.40, for

7


wind speeds of 7 and 20m/s, respectively, whose equivalent values in SI units are 0.015m/sand 0.300m/s. Hence, the blade flapping adds 0.2% and 1.5% instantaneously to the axialcomponent, respectively.

The FFTs of the flapping signal obtained from the last two rotor revolutions are pre-sented in Figures 7 (c) and (f). The frequency multiples of the blade-passing (2.4Hz) areincluded, as well as the first four natural frequencies included in the structural model.The highest peak corresponds to the second harmonic (4.8Hz).

(o)

(%

c)

0 90 180 270 360-1.85

-1.8

-1.75

-1.7

-1.65

-1.6

-1.55

Blade 1Blade 2 +180o

(o)

d/d

t

0 90 180 270 360-0.03

-0.02

-0.01

0

0.01

0.02

0.03


f (Hz)

A (

)

0 4 8 12 16 20 24 280

0.01

0.02

0.03

0.04

0.05HarmonicsNatural freq.Blade 1Blade 2

(a) (b) (c)

(o)

(%

c)

0 90 180 270 360-5.5

-5

-4.5

-4

-3.5

-3

-2.5

-2


(o)

d/d

t

0 90 180 270 360

-0.4

-0.2

0

0.2

0.4

0.6Blade 1Blade 2 +180o

f (Hz)

A (

)

0 4 8 12 16 20 24 280

0.2

0.4

0.6

0.8

1HarmonicsNatural freq.Blade 1Blade 2

(d) (e) (f)

Figure 7: Flapping motion of the tip leading edge of the NREL Annex XX blades, at wind speeds of7m/s (Top) and 20m/s (Bottom). (a,d) Flapping amplitudes (%c). (b,e) Flapping derivatives. (c,f)Flapping FFTs. Ψ =0 deg. indicates that blade 1 is at the top and blade 2 is aligned with the tower. Theharmonics correspond to multiples of the blade passing frequency fn = nf1 (f1 =2.4Hz). The naturalfrequencies are: fn1 = 7.34, fn2 = 8.79, fn3 = 20.13, fn4 = 26.03.

Figure 8 shows the amplitudes and the derivatives of the edgewise motion. Note that,for easier visualisation, the amplitudes of blade 2, although negative, are shown withpositive sign and the 180 degrees off-set is also applied. Compared to the flapping motion,the edgewise amplitudes are one order of magnitude smaller and the same delay observedin the flapping motion is presented here. The maximum addition to the tangential tipvelocity component (37.7m/s) when the blades have passed in front of the tower is 0.005%and 0.008% for wind speeds of 7 and 20m/s, respectively, as shown in the derivatives inFigures 8 (b) and (e). From the FFTs presented in Figures 8 (e) and (f), one can observed

8


a highest amplitude peak at 6Hz, corresponding to five times the rotational frequency.

(o)

(%

c)

0 90 180 270 3600.21

0.22

0.23

0.24

0.25

0.26

Blade 1-(Blade 2 +180 o)

(o)

d/d

t

0 90 180 270 360-0.01

-0.005

0

0.005

0.01


f (Hz)

A (

)

0 4 8 12 16 20 24 280

0.001

0.002

0.003

0.004

0.005


(a) (b) (c)

(o)

(%

c)

0 90 180 270 3600.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Blade 1- (Blade 2 +180 o)

(o)

d/d

t

0 90 180 270 360-0.15

-0.1

-0.05

0

0.05

0.1

0.15


f (Hz)

A (

)

0 4 8 12 16 20 24 280

0.02

0.04

0.06

0.08


(d) (e) (f)

Figure 8: Edgewise motion of the tip leading edge of the NREL Annex XX blades, at wind speeds of7m/s (Top) and 20m/s (Bottom). (a,d) Edgewise amplitudes (%c). (b,e) Edgewise derivatives. (c,f)Edgewise FFTs. Ψ =0 deg. indicates that blade 1 is at the top and blade 2 is aligned with the tower. Theharmonics correspond to multiples of the blade passing frequency fn = nf1 (f1 =2.4Hz). The naturalfrequencies are: fn1 = 7.34, fn2 = 8.79, fn3 = 20.13, fn4 = 26.03.

A 3D view of the region closed the the blade tip is presented in Figure 9, for thereference blade (blade 1), where the differences between the rigid and elastic blades canbe observed, as well as the difference in deformation between the two wind speed cases.

(a) 7m/s. (b) 20m/s.

Figure 9: Comparison between rigid and elastic blades at the tip region.

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4.3 Study of the blade loads

The effect of aeroelasticity in the integrated thrust, torque and aerodynamic powerfor the reference blade (blade 1) is presented in Figure 10, for a full revolution. In theCFD, an averaging over the last two rotor revolutions was carried out and error barswith standard deviation are included. The integration of the loads for both CFD andexperiments was performed using the locations of the measurement pressure taps at fiveblade stations and summing them up, considering the covered area and dynamic pressure.The S07 and S20 experimental datasets [10] were employed for comparison.

(o)

T (

N)

0 60 120 180 240 300 360475

500

525

550

575

600

625

650EXP+/- CFD RigidCFD Elastic

(o)

Q (

Nm

)

0 60 120 180 240 300 360275

300

325

350

375

400

425

450


(o)

Po

wer

(kW

)

0 60 120 180 240 300 3602.2

2.4

2.6

2.8

3

3.2

3.4EXPCFD RigidCFD Elastic

(a) (b) (c)

(o)

T (

N)

0 60 120 180 240 300 3601200

1300

1400

1500

1600

1700

1800


(o)

Q (

Nm

)

0 60 120 180 240 300 360100

200

300

400

500

600

700

800


(o)

Po

wer

(kW

)

0 60 120 180 240 300 3601.5

2

2.5

3

3.5

4

4.5

5

5.5

6

6.5EXPCFD RigidCFD Elastic

(d) (e) (f)

Figure 10: Comparison with the experiments of the single blade integrated thrust (left), torque (middle)and aerodynamic power (right), including averaged values and standard deviation, for the rigid and elasticreference blades and wind speed of 7m/s (top) and 20m/s (bottom). At Ψ = 0 deg. the blade is at 12o’clock and at Ψ = 180 deg. is in front of the tower.

At 7m/s, shown at the top of Figure 10, a deficit of approximately 5% in the integratedquantities is observed as a result of the blade passing in front of the tower at an azimuthangle of 180 degrees. This is due to a change in pressure between the blade and thetower and a change in the angle of attack as a consequence of the air being deflectedwhen is hit by the tower. Overall, there is good agreement with the experiments, withunder-predictions of approximately 4% thrust and 10% in the torque and aerodynamicpower, which are consistent all over the blade, as can be seen in Figure 11 (a), where thecontribution of each section to the overall loads is shown.

10


Tse

ct (

N)

Qse

ct (

Nm

)

0

20

40

60

80

100

120

140

160

180

200

220

0

15

30

45

60

75

90

105

120T (EXP)T (CFD Rig.)T (CFD El.)Q (EXP)Q (CFD Rig.)Q (CFD El.)

46.6%R 63.3%R30%R 95%R80%R

Tse

ct (

N)

Qse

ct (

Nm

)

0

50

100

150

200

250

300

350

400

450

500

-30

0

30

60

90

120

150

180

210

240T (EXP)T (CFD Rig.)T (CFD El.)Q (EXP)Q (CFD Rig.)Q (CFD El.)

46.6%R 63.3%R30%R 95%R80%R

(a) 7m/s. (b) 20m/s.

Figure 11: Sectional integrated thrust and torque at five blade sections for rigid (Rig.) and elastic (El.)cases and wind speeds of (a) 7m/s and (b) 20m/s.

At 20m/s, the experiments are more oscillatory and do not reveal a clear deficit atthe region of the blade-tower interaction, Figures 10 (d) and (e), while in the CFD ismuch clearer. In this case, the dip in the integrated quantities is delayed by 20 degreesapproximately from the 180 degrees azimuthal position. The averaged values of thrustare in very good agreement with the experiments, falling inside the range of error of theexperiments, while the torque is overpredicted by 10% approximately from the measuredmean value. Similiar issues were reported in the literature [7], good agreements withthrust and differences in torque predictions. The contribution of each section to theintegrated loads plotted Figure 11 (b) shows that the source of disagreement on theintegrated torque is the section close to the root at 30%R and the section at 80%. Atthis wind conditions, the predicted deformations were higher and oscillated more rapidlythan the lower wind speed case, which resulted in an increase of the integrated torqueand therefore aerodynamic power of 13% approximately from the rigid case, as shown inFigures 10 (e) and (f). The section that contributes the most to this change is at the tipof the blade (95%R), where there is a change of sign of the integrated torque, see Figure11. This is the result of the fast oscillation at the tip.

5 CONCLUSIONS

The current paper presented a fully coupled dynamic CFD-CSD method, applied to theNREL Phase VI wind turbine. At wind speed of 7m/s, the flow was attached practicallyall over the blade, and 20m/s, the flow was stalled. Due to the proximity of the rotor tothe tower, a deficit on the thrust and torque values was observed due to the blade passage,which was in good agreement with the experiments. Flapping and edgewise deflectionswere captured with the aeroelastic method, being the former the most significant one,and maximum deflections were observed after the blades had passed in front of the towerand with 20 and 40 degrees of delay, at wind speeds of 7 and 20m/s, respectively. Larger

11


deflections were obtained at 20m/s than at 7m/s wind speed. The effect of the deforma-tions on the loads was found to be very small at 7m/s, obtaining differences of less than1% in the averaged thrust and torque, between the rigid and elastic blades. At 20m/s,conversely, the torque on the elastic blades showed a 13% increment from the rigid ones,which was attributed to the rapid blade oscillation.

In the future, it would be interesting to apply this method to blades of real windturbines, where the aeroelastic effects may be more pronounced.

ACKNOWLEDGEMENTS

The financial support by the Renewable Energy Centre of Spain (CENER) and theUniversity of Liverpool is gratefully acknowledged. Access to the HPC facilities ”Polaris”at Leeds University and ”Chadwick” at University of Liverpool is also acknowledged.

REFERENCES

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[7] S. Gomez-Iradi, R. Steijl and G.N. Barakos, Development and Validation of a CFDTechnique for the Aerodynamic Analysis of HAWT, J. Solar Energy Engineering-Transactions of the ASME (2009) 131(3):031009.

[8] M. Carrión, M. Woodgate, R. Steijl, G. Barakos, S. Gomez-Iradi and X. Munduate,CFD Analysis of the Wake behind the MEXICO Rotor in Axial Flow Conditions,Wind Energy Journal, Accepted February 2014.

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