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CFD Simulations of the Mexico Wind Tunnel and Wind Turbine

Réthoré, Pierre-Elouan Mikael; Zahle, Frederik; Sørensen, Niels N.; Bechmann, Andreas

Published in:Proceedings

Publication date:2011

Document VersionPublisher's PDF, also known as Version of record

Link back to DTU Orbit

Citation (APA):Réthoré, P-E. M., Zahle, F., Sørensen, N. N., & Bechmann, A. (2011). CFD Simulations of the Mexico WindTunnel and Wind Turbine. In Proceedings European Wind Energy Association (EWEA).

https://orbit.dtu.dk/en/publications/b2ab7f2a-4023-481e-b9e3-a24469aaebe9

CFD model of the MEXICO wind tunnel

P.-E. Réthoré∗, N. N. Sørensen, F. Zahle, A. Bechmann and H. A. Madsen

Wind Energy Division, Risø DTU, DK-4000 Roskilde, Denmark.∗ pire@risoe.dtu.dk. tel: +45 21331293.

Abstract

The MEXICO Experiment is reproduced in CFD,including the geometry of the wind tunnel and thewind turbine rotor. The wind turbine is modelledboth as a full rotor and as an actuator disc. Vari-ous questions regarding the wind tunnel effects onthe measurements are investigated. As in a previ-ous work carried out without modelling the windtunnel, the CFD methods are found to give satisfy-ing agreement with the axial velocity deficit in thewake. However, confirming the previous work, theblade loadings estimated from CFD are found tobe consistently larger than the one estimated frommeasurements. In order to investigate further thisissue, the loadings estimated from measurement areused with an actuator disc model. This approachgives a too small wake deficit in comparison withthe measurements, which tends to agree with thefull rotor computation results.

1 Introduction

The EU FP5 project ’Model EXperiments In COn-trolled COnditions’ or ’MEXICO’ [13] was a windtunnel experiment campaign leaded by the Energyresearch Center of the Netherland (ECN). A 4.5 mdiameter fully instrumented wind turbine was setup in the 9.5×9.5 m open jet wind tunnel of theGerman Dutch Wind tunnel Organization (DNW).Some ’breathing slots’ were introduced behind thecollector to avoid flow recirculation. The forcesacting on the blades were estimated using pressuresensors at 5 sections on the blades. The flowupstream and downstream of the wind turbine wasobserved using Particle Image Velocimetry (PIV).The purpose of this experiment was to provide highquality experimental data to validate various typesof wind turbine models. An exhaustive literaturelist concerning the experiment and the related

analysis is available on the MEXICO Experimentwebsite [1].

Risø DTU has developed a set of Wind EnergyCFD tools to model the flow passing through windturbines [9, 15] or in complex terrain [2, 14]. RisøDTU has therefore been interested from the begin-ning to participate in the MEXICO Experimentin order to compare the measurements with ourdifferent models.

When dealing with new types of wind tunnelexperiments many questions arise on the possibleunexpected influence of the wind tunnel on themeasurements. Some of the questions addressedin this study are as follow. How far downstreamand upstream of the wind turbine is the flowunaffected by the wind tunnel geometry? Do the’breathing slots’ have a noticeable influence on themeasurements? Is the flow influenced by the windtunnel room geometry? In order to investigatethose questions the geometry of the DWN windtunnel is used as a background mesh to the CFDcomputation.

Moreover, previous CFD Full Rotor (FR)calculations where done by Bechmann et al. [3]on the MEXICO wind turbine rotor, withoutconsidering the wind tunnel. These results showthat it is possible to obtain a satisfying fit withthe flow measurements, while at the same time tohave loadings on the wind turbine blades that aresignificantly larger than what the measurementspredict. This could potentially indicate that theestimation of the wind turbine blade loading havebeen underestimated during the experiments. TheActuator Disc (AD) method [12], which takes theloadings from the MEXICO experiment, is used inthis work to investigate this issue.

1

The rest of the paper is organized as follow. First,a brief description of the different methods usedin this work. Then, the presentation of differenttest cases run and associated results. Finally, a dis-cussion of different issues such as the wind tunnelReynolds Number independence, the flow asymme-try, the wind tunnel perturbations, the influence ofthe breathing slots and of the jet oscillation. Fi-nally, the mismatch between blade loadings andflow features is addressed.

2 Method

2.1 Flow Solver

The flow solver used in this work, EllipSys, is anin-house general purpose CFD code developed atRisø DTU [14] and DTU MEK [7]. It is a flowsolver based on a finite-volume spatial and tem-poral discretization of the incompressible Navier-Stokes Equations formulated in general curvilinearcoordinates. The variables are collocated in the cellcenters to enable computations using complex geo-metrical meshes. The pressure correction method isbased on the Rhie-Chow algorithm, which is mod-ified for the treatment of the body forces of theactuator disc model [10] and is accelerated using amultigrid technique. The flow is solved successivelyover three levels of discretization in order to accel-erate the convergence and to ensure a grid indepen-dent solution [7]. The equations can be discretizedusing different schemes (see Section 2.3 & 2.4). Forthe full rotor computation, the PISO [4] method isused to solve the Navier-Stokes Equations system,while for the actuator disc method, the SIMPLE [8]method is used. The flow equations are discretizedusing a QUICK formulation [5] in both methods.The Reynolds stresses are modelled in the Navier-Stokes equations using the eddy-viscosity assump-tion and a k-ω-SST [6] turbulence model.

2.2 Wind Tunnel Mesh

Most of the human work time of this project wasspent on meshing the DWN wind tunnel. Theshape of the nozzle and collector are confidentialand a Non Disclosure Agreement was signed withDWN in order to obtain them. In order to be ableto freely publish the results the decision was madeto not show the final shapes of the nozzle andcollectors. All the figures illustrating those partsare therefore whether slightly altered, obstructedor a free ’artistic’ representation (done prior to

Figure 1: Horizontal view of the mesh blocks.

Figure 2: Perspective view of the mesh blocks.

obtaining the confidential information), and shouldnot be considered as realistic in any way. Thesimulations are, however, carried out using thecomplete nozzle and collector shapes.

The wind tunnel is meshed using the soft-ware PointWise as 386 323-cell structured blocks(around 12M cells). The support structure of thewind turbine rotor, as well as the support structureof the collector are not considered in this study.These structures are rather large blunt bodies,and should have an important impact on the flowbehavior around these regions. It is thereforeassumed that the region of interest and the overallloads on the wind turbine blade are not influencedby these support structures. Some details ofthe mesh structure are illustrated on Fig.1-3.Note that in these figures the blocks illustratedhave not yet been subdivided into 323-cell elements.

The inlet and outlet of the domain are extended,and the cells size are gradually stretched, expand-ing towards the inlet and outlet (see Fig.1). This isdone in order to avoid to have some influence fromthe boundary condition over the zone of interest,and to enforce a numerical dissipation to avoid flowstructures to create unstability while passing theoutlet. As these regions are nowhere near the in-teresting locations their geometry should have littleinfluence on the results.

The wall boundary conditions are taken as

2

Figure 3: Detail of the collector lips meshing. The’breathing slots’ are visible on the right side of themesh.

slip condition (symmetry). This is done to avoidresolving the boundary layer at the wall surface forspeeding up both the meshing and computationalexpenses. The shortcoming of this approach is thatthere is not any development of a boundary layeron the walls of the room, nozzle and collector. Theassumption made is therefore that this boundarylayer does not influence the region of the flowwhere the measurements are made.

The “breathing slots“ located at the exit of thecollector are taken into account in the mesh geom-etry (see Fig.3). In order to assess their effect, avariation of the wind tunnel mesh is done withoutthe slots (referred later as ”WT-no hole”).

2.3 Full Rotor Computation

In a previous work by Bechmann et al., the windturbine rotor was mesh with an o-geometry. For anin-depth description of the method used to meshthe surface of the rotor and compute the MEXICOrotor, without wind tunnel, see [3].In the current work, the full geometry of the MEX-ICO wind turbine rotor, excluding the spinner,hub, tower and support structured, is meshedand is added to the wind tunnel mesh throughan overset grid methodology [15]. Note that thesurface mesh of the rotor is the same as usedin [3]. Three overset meshes are used in additionto the wind tunnel to smoothly interpolate fromthe very fine rotor mesh to the coarser backgroundmesh (see Fig.4. One cylindrical mesh close tothe turbine that rotates with the rotor mesh, andone coarser, which is fixed relative to the windtunnel mesh and extends up to one rotor diameterdownstream. In the case of the mesh withoutwind tunnel, a Cartesian background mesh is used

Figure 4: Detail of the full rotor computation mesh.top: front view. bottom: side view.

instead of the wind tunnel mesh. The rotor mesh isdesigned to have a maximum cell size at the bladesurface so that y+ < 2. The total mesh composedof the background wind tunnel mesh describedin the previous section and the three successiverefinement meshes represents in total 798 323-cellblocks (26M+ cells). The code runs in transientmode at 7.5 hours per revolution on 160 CPUs.The result shown are run for 10 revolutions, so 3.2days.

Fig.5 illustrates the full rotor computation of theMEXICO rotor in the DWN wind tunnel.

2.4 Actuator Disc Model

The actuator disc model [12] is spreading the bladeforces over a disc and applying them into the windtunnel background mesh. The forces are treatedin a special way to avoid pressure-velocity decou-pling [10]. In all the actuator disc simulations, theforces are splined from the 5 wind turbine bladepressure sensor measurements (see Fig.6).

Two types of solutions are considered, an un-steady Detached Eddy Simulation (DES) solution

3

Figure 5: Full rotor computation of the MEXICOrotor in the DWNwind tunnel. Vorticity iso-surfaceand axis velocity colour contour in an horizontalplane at hub height. The wind tunnel geometry isvisible in transparent.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1−100

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Measurements 24 m/s

AD 24 m/s

Figure 6: Description of the different wind turbineblade loadings. The Actuator Disc (AD) loadingsare splined from the measurements points, whilethe Full Rotor (FR) computations loadings are es-timated from the simulation results.

and a steady state solution. The transient solu-tion is run with a time step of ∆t = 0.01 sec, for2000 iterations using 6 subiterations, which takesabout 16h on 100 CPUs. The 2000 iterations onthe steady state computation only takes 2-3 hourson 100 CPUs.

3 Results

3.1 Runs

With the different wind turbine models and typesof mesh, 7 different types of runs are calculated atthe 3 different wind speeds of the experiment (10,15 and 24 m/s).

• Wind tunnel mesh without wind turbinesteady state (Tunnel).

• Actuator disc model with wind tunnel steadystate (AD-WT).

• Actuator disc model with wind tunnel withoutbreathing slot steady state (AD-WT-noSlot).

• Actuator disc model without wind tunnelsteady state (AD-noWT).

• Actuator disc model with wind tunnel un-steady DES (AD-DES).

• Full rotor computation with wind tunnel un-steady RANS (FR-WT).

• Full rotor computation without wind tunnelunsteady RANS transient (FR-noWT).

3.2 Streamwise Sections

Fig.7 presents the axial velocity in an horizontalline passing through the wind tunnel, withoutturbine, at hub height and z/D = 0.33 for variousinlet velocity.

Fig.8 shows the axial velocity in an horizontalline passing through the wind tunnel at hub heightand z/D = 0.82132 for the different wind turbinemodels, with and without the wind tunnel, for dif-ferent inlet wind speed and compare them with therelevant wind speed measurements.

Fig.9 presents a comparison between differentsteady state actuator disc runs with different kindof meshes (without wind tunnel, and win tunnelwith and without breathing slots).

4

−10 −4.07 −1.77 0 2.98 6.03 10

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AD − WT − 10 m/s

AD − WT − 15 m/s

AD − WT − 24 m/s

FR − WT − 10 m/s

FR − no WT − 10 m/s

Experiment 10 m/s

Experiment 15 m/s

Experiment 25 m/s

Figure 8: Comparison of different runs with respective measurements. With wind tunnel (WT) and without(no WT). With a steady state actuator disc (AD) and with an unsteady full rotor computation (FR).

Figure 7: Wind tunnel with wind turbine of con-stant CT at different wind speeds, collapsing whennormalized. The wind speed indicated is the inflowwind speed at the inlet boundary. They are nor-malized with a constant ratio that would give unityat the wind turbine position, when no wind turbineis present.

−10 −4.07 −1.77 0 2.98 6.03 10

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Tunnel & DiscTunnel & No discNo tunnel & DiscTunnel (No Hole) & Disc

Figure 9: Comparison of different steady state actu-ator disc runs with respective measurements. Withand without wind tunnel. With the ’breathingslots’ and without (no hole)

5

Figure 10: Transverse sections at different positionupstream and downstream of the wind turbine fromdifferent types of simulations.

Figure 11: Actuator disc simulation of the MEX-ICO rotor (AD-WT). Vorticity colour contour in anhorizontal plane at hub height.

3.3 Transverse Sections

Fig.10 shows the axial velocity along transversesections at different positions downstream and up-stream of the wind turbine (animated only in thedigital version), including regions of perturbed flow.Different steady-state actuator disc simulations arepresented: actuator disc with and without windtunnel, actuator disc with a wind tunnel withoutbreathing slots (no hole) and a simulation with awind tunnel without actuator disct.

3.4 Contourlines

Fig.11 illustrates the vorticity contouts at hubheight of a steady state actuator disc model withan inflow wind speed of 10 m/s.

Figure 12: Actuator disc simulation of the MEX-ICO rotor. Axial velocity colour contour on a hor-izontal plane at hub height. Frames from the DESanimation [11].

3.5 DES animation

A video of the unsteady animation (AD-DES) isavailable online [11]. An extract of it is also visiblein the digital version of this article (Fig. 12).

4 Discussion

4.1 Reynolds Number independence

Fig.7 shows that the wind tunnel simulation isReynolds Number independent. This shows thatthe jet development is not dependent of the inflowvelocity. However, this mesh has a slip boundarycondition on the wall, and therefore no boundarylayer is developing. A mesh with a no-slip bound-ary condition might not be Reynolds number inde-pendent.

4.2 Flow Asymmetry

The horizontal asymmetry of the wind tunnel ge-ometry (visible in e.g. Fig.1) seems to generate awider recirculation zone on one side than on theother. This effect could explain why the wake en-tering the collector seems to be bended in Fig.11.It could also explain some lateral forces recorded onthe wind turbine support structure.

4.3 Wind Tunnel Perturbations

The difference between the actuator disc simula-tions with and without wind tunnel seem to indi-cate that the wind tunnel collector can influence

6

the wake measurements as soon as 1.5 rotor diame-ter downstream (see Fig.9-10). Similarly, the nozzlehas an influence on the flow that cannot be ignoremore than 1 rotor diameter upstream. Those ob-servations are also visible while looking at the fullrotor computations, Fig.8.

4.4 Breathing Slots Effect

From analyzing the results presented in Fig.9 and10, the ’breathing slots’ do not seem to have a sig-nificant effect in the region where the wind tunneldoes not affect the flow (x/D ∈ [−1, 1.5]).

4.5 Jet Oscillation Effect

In the DES animations [11] there is a clear oscilla-tion of the jet interface going in and out of the col-lector lips. These oscillations seem to have a signif-icant effect on the wake dynamics (see also Fig.12).Nonetheless, while looking at the full rotor com-putation unsteady-RANS animation, this jet inter-face was not oscillating. The difference betweenthe two simulations is that the unsteady-RANS al-lows a build up of the eddy-viscosity and the tur-bulence at the jet interface that could damp andaccount for those oscillations. In the DES simula-tions, there is a limit put on the turbulent length-scale size that effectively prevent an increase ofeddy-viscosity. Nonetheless, it remains unclear ifthose oscillations did actually appear in the exper-iments and if they indeed had such a significantimpact on the wake dynamics. More work needs tobe done on this issue to answer this question.

4.6 Blade Loading and Flow Features

The flow characteristics found with the actuatordisc model, based on the forces from the measure-ments, do not give satisfying results in comparisonwith the measurements. They systematically un-derpredict the wake deficit in comparison with boththe measurements and the full rotor computations.This seems to indicate that the loadings estimatedfrom the pressure sensors are not large enough toobtain the measured velocity deficits. This tends toagree with the results of Bechmann et al. [3] thatindicates that the full rotor computations obtainsignificantly higher loadings (see also Fig.6).The full rotor computation carried out with andwithout the wind tunnel give very close results inthe region of comparison. This furthermore indi-cates that the wind tunnel effect cannot explain the

mismatch between the forces measured on the bladeand the axial velocity measurements.

5 Conclusion

The open wind tunnel of the MEXICO experimentwas successfully modelled in CFD using two typesof wind turbine models (Full rotor computation andactuator disc).The results show that the effect of the wind tunnelover the region of comparison in the wake shouldnot be significant. Similarly, the breathing slotsare not found to have a significant influence in theregion of interest.However the DES analysis showed that there couldbe an oscillation of the wind tunnel jet interfacethat could potentially create a significant oscilla-tion of the wake. It is unclear if this effect canbe observed in the MEXICO measurements and ifthey had an impact on the quality of the experi-ment. More work should be focussed on this ques-tion, as it raises a potential issue with future openwind tunnel experiments of wind turbine wakes.Finally there seems to be a mismatch between theblade loadings measured and the axial velocity mea-surements. Both the full rotor computation and theactuator disc model cannot match both results atthe same time satisfyingly. This could potentiallyindicate an under estimation of the blade loadings.

Acknowledgement

The authors are grateful for the IEA projectMEXNEX and the DSF Flow center for financingthis work, DNW for providing the wind tunnel ge-ometry and J.G. Schepers, K. Boorsma and H. Snelfrom ECN and for providing the wind turbine mea-surements.

References

[1] MEXICO experiment web site.http://www.mexnext.org/resultsstatus.

[2] A. Bechmann. Large-Eddy Simulation of At-mospheric Flow over Complex Terrain. PhDthesis, DTU-MEK, Denmark, 2007.

[3] A. Bechmann, N. N. Sørensen, and F. Zahle.CFD Simulation of the MEXICO Rotor Wake.Wind Energy (in revision).

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http://www.mexnext.org/resultsstatus

[4] R. I. Issa. Solution of the implicitly discre-tised fluid flow equations by operator-splitting.Journal of Computational Physics, 62(1):40–65, January 1986.

[5] B. P. Leonard. A stable and accurate convec-tive modelling procedure based on quadraticupstream interpolation. Comp. Meth. in Appl.Mech. and Engrng., 19:59–98, 1979.

[6] F. R. Menter. Zonal two equation k- turbu-lence models for aerodynamic flows. AIAAJournal, (93-2906), 1993.

[7] J. A. Michelsen. Basis3D - a platform for de-velopment of multiblock PDE solvers. Techni-cal report AFM 92-05, Technical University ofDenmark, Lyngby, 1992.

[8] S. V. Patankar and D. B. Spalding. A calcu-lation procedure for heat, mass and momen-tum transfer in three-dimensional parabolicflows. Int. J. Heat Mass Transfer, 15:1787–1972, 1972.

[9] P.-E. Réthoré. Wind Turbine Wake in Atmo-spheric Turbulence. PhD thesis, Aalborg Uni-versity - Risø DTU, October 2009. [PDF].

[10] P.-E. Réthoré and N. N. Sørensen. Ac-tuator disc model using a modified Rhie-Chow/SIMPLE pressure correction algorithm.EWEC Brussels, 2008. [PDF].

[11] P.-E. Réthoré, N. N. Sørensen, and H. A.Madsen. Wind tunnel model of the mex-ico experiment. Wind Energy Research, 2010.http://windenergyresearch.org/?p=81.

[12] P.-E. Réthoré, N. N. Sørensen, and F. Zahle.Validation of an Actuator Disc Model. EWECWarsaw, 2010.

[13] J. G. Schepers and H. Snel. Model experimentsin controlled conditions, final report. Technicalreport, Energy Research Center of the Nether-lands, ECN. ECN-E-07-042, 2007. [PDF].

[14] N. N. Sørensen. General Purpose Flow SolverApplied to Flow over Hills. PhD thesis, Tech-nical University of Denmark, 1994.

[15] F. Zahle. Wind Turbine Aerodynamics Usingan Incompressible Overset Grid Method. PhDthesis, Imperial College, London, 2007.

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http://www.risoe.dtu.dk/rispubl/reports/ris-phd-53.pdfhttp://www.ewec2008proceedings.info/statscounter.php?id=5&IDABSTRACT=225http://windenergyresearch.org/?p=81http://www.ecn.nl/docs/library/report/2007/e07042.pdf

1 Introduction2 Method2.1 Flow Solver2.2 Wind Tunnel Mesh2.3 Full Rotor Computation2.4 Actuator Disc Model

3 Results3.1 Runs3.2 Streamwise Sections3.3 Transverse Sections3.4 Contourlines3.5 DES animation

4 Discussion4.1 Reynolds Number independence4.2 Flow Asymmetry4.3 Wind Tunnel Perturbations4.4 Breathing Slots Effect4.5 Jet Oscillation Effect4.6 Blade Loading and Flow Features

5 Conclusion

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