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Extended Abstracts for Euromech Colloquium 508 on Wind Turbine Wakes 20-22 October 2009 E.T.S.I. Industriales Universidad Politécnica de Madrid Madrid Chairman: Antonio Crespo (UPM) Co-Chairman: Gunner Chr. Larsen (Risoe-DTU) Coordinator: Emilio Migoya (UPM)

Euromech Colloquium 508

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Page 1: Euromech Colloquium 508

Extended Abstracts for Euromech Colloquium 508 on

Wind Turbine Wakes

20-22 October 2009

E.T.S.I. Industriales

Universidad Politécnica de Madrid Madrid

Chairman: Antonio Crespo (UPM) Co-Chairman: Gunner Chr. Larsen (Risoe-DTU)

Coordinator: Emilio Migoya (UPM)

Page 2: Euromech Colloquium 508
Page 3: Euromech Colloquium 508

Extended Abstracts for Euromech Colloquium 508 on

Wind Turbine Wakes

20-22 October 2009

E.T.S.I. Industriales

Universidad Politécnica de Madrid Madrid

Chairman Antonio Crespo (UPM) [email protected] Co-Chairman Gunner Chr. Larsen (Risoe-DTU) [email protected] Coordinator Emilio Migoya (UPM) [email protected]

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Edita e imprime: Sección de Publicaciones de la Escuela Técnica Superior de Ingenieros Industriales. Universidad Politécnica de Madrid ISBN: 978-84-7484-220-3 Depósito Legal: M-41352-2009

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Euromech Colloquium 508 Madrid, 20-22 October 2009 Wind turbine wakes are an interesting topic of study, because the momentum deficit and the increased level of turbulence created by turbines in a wind farm may cause a reduction in power output and an increase in unsteady and fatigue loads on downstream located machines. Besides, a good knowledge of the aerodynamics in the near wake is essential to understand the physics of power extraction by wind turbines. The topics to be addressed will include:

• Numerical models of wind turbine wakes - single wakes as well as multiple wakes in wind farms.

• Turbulence closure models. • Actuator disk and actuator line models. • Experimental work, based on both wind tunnel experiments and full scale field

experiments and flow visualization. • Tip vortex properties. • Characteristics of the added turbulence created in the wake. • Influence of atmospheric stability. • Influence of topography. • Wake meandering. • Fatigue and loads. • Offshore wind farms. • Strategies for control based on wind turbine wakes.

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INDEX Tuesday, 20 October 08:30 Registration, Welcome + Opening address. Jesús Felez, Director of the ETSI Industriales I Wake models. Multiple wakes in wind farms. ROOM D 09:00 Extensions of the Jensen wake model for wind farm flows. E. Hedevang……….… 1 09:15 Enhanced CFD Modelling of Wind Turbine Wakes. J.M. Prospathopoulos, E.S. Politis, K.G. Rados, P.K. Chaviaropoulos…………………………………………………. 3 09:30 Universal Benchmarks for Wind Turbine Wake and Wind Farm Models. Patrick Moriarty, Rebecca Barthelmie……………………………………………………………... 6 09:45 Stochastic simulation to study wake meandering using UPMPARK. E. Migoya, A. Jiménez, F. Manuel, A. Crespo…………………………………………………………….. 8 10:00 Fast linearized models for wind turbine wakes. Søren Ott………………………….. 11 10:15 Discussion 10:30 Coffee Break II Turbulence closure models. ROOM D 11:00 Comparison of turbulence models for the CFD simulation of wind turbine wakes in the Atmospheric Boundary Layer. D. Cabezón, J. Sanz, I. Martí, A. Crespo, E. Migoya… 14 11:15 Energy Preservation in the Numerical Calculation of Wind Turbine Wakes. B. Sanderse, B. Koren ………………………………………………………………………... 16 11:30 Turbulence closure strategies for modelling wind turbines wake. Pierre-Elouan Réthoré, Niels N Sørensen…………………………………………………………………. 19 11:45 Analysis of the wake meandering using a LES method. A. Jiménez, E. Migoya, J. García, A. Crespo, J.L. Prieto……………………………………………………………… 20 12:00 Validation of wake analytical models of WindSim in neutral and stable conditions in a offshore. Giorgio Crasto, Arne Reidar Gravdahl……………………………………… 22 12:15 Discussion 12:30 Lunch III Actuator disk and actuator line models. Aerodynamics. Near wake. ROOM D 14:00 Numerical Simulations of Wake Interaction between Two Wind Turbines at Various Inflow Conditions. N. Troldborg, G.C. Larsen, H.A. Madsen……………………. 23 14:15 On actuator disc force fields generating wake vorticity. GA.M. van Kuik, A.H. van Zuylen……………………………………………………………………………………… 26 14:30 Meandering Wake Characteristic Derived from Actuator Line Simulations of Wind Turbine Wakes. Robert Mikkelsen, Jens N. Sørensen, Stig Øye…………………………... 29 14:45 Actuator disc momentum theory for low lambda rotors. Jens Nørkær Sørensen, Gijs van Kuik......................................................................................................................... 30 15:00 Use of actuator disk and actuator surface methods for the aerodynamic modeling of wind turbines: A review. Christian Masson, Christophe Sibuet-Watters, Simon-Philippe Breton, Jonathon Sumner…………………………………………………………………... 32 15:15 Discussion 15:30 Coffee Break

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IV Influence of atmospheric stability and topography. ROOM D 16:00 The dependence of wake losses on atmospheric stability characteristics G.C. Larsen, T.J. Larsen, H.Aa. Madsen, J. Mann, A. Peña, R. Barthelmie and L. Jensen……... 35 16:15 Do wind farms influence large scale turbulence? G.C. Larsen, J. Mann, T.A. Ighil, A.S. Mouritzen………………………………………………………………………...…… 38 16:30 RANS simulations of a wind-farm with the application of the actuator disc concept. Giorgio Crasto, Francesco Castellani, Arne Reidar Gravdahl………………………….….. 41 16:45 Mesoscale and turbulence effects on wind farms. Julian Hunt……………………… 42 17:00 Numerical simulations of the turbulent logarithmic layer. Javier Jiménez…………. 43 17:15 Wind tunnel simulation of the wakes of large wind turbines in off-shore stably stratified flow. F. Pascheke, P. E. Hancock………………………………………………... 44 17:30 Large Eddy Simulation study of fully developed wind-turbine array boundary layers. Marc Calaf, Charles Meneveau, Johan Meyers…………………………………….. 45 17:45 Discussion Wednesday, 21 October V Experimental work, based on both wind tunnel experiments and full scale field experiments (first session). ROOM D 09:00 Comparison and Validation of BEM and Free Wake Unsteady Panel Model with the MEXICO Rotor Experiment. Daniel Micallef, Menno Kloosterman, Carlos Ferreira, Tonio Sant, Gerard van Bussel…………………………………………………………….. 46 09:15 Experimental and numerical investigation of the 3D VAWT wake. Carlos Ferreira, Claudia Hofemann, Gijs van Kuik, Gerard van Bussel……………………………………. 49 09:30 Development of a process chain for a detailed wake simulation of horizontal axis wind turbines. K. Meister, Th. Lutz, E. Krämer……………………………..………..…… 52 09:45 LiDAR measurements of full scale wind turbine wake characteristics. Kurt S. Hansen, Gunner Chr. Larsen, Karen Enevoldsen, Jakob Mann……………………...…….. 55 10:00 Decaying Coherent Eddy Structures and Turbulent Fluctuations in Wind Turbine and Wind Farm Wakes - analysis of airborne measurements. Abha Sood, Jens Bange…… 57 10:15 Discussion 10:30 Coffee Break

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VI Experimental work, based on both wind tunnel experiments and full scale field experiments (second session). ROOM D 11:00 Temporal and spatial study of the meandering phenomenon. G. España, S. Aubrun, S. Loyer, P. Devinant………………………………………………………………………. 59 11:15 Influence of topography and wakes on wind turbulence. Measurements and interpretation of results. A. Jiménez, E. Migoya, M. Esteban, J. García, D. Giménez, A. Crespo……………………………………………………………………………………… 61 11:30 Advances in wind tunnel testing of wind farm. Sebastián Franchini, Álvaro Cuerva Tejero and Oscar López García……………………………………………………………. 62 11:45 Wake measurements of a multi-MW wind turbine with long range lidar Y. Käsler, S. Rahm, R. Simmet, J.-J. Trujillo…………………………………………………………. 63 12:00 Measurements of a multi-MW turbine near-wake using lidar from the nacelle. J.J. Trujillo, F. Castellote, O. Bischoff, M. Hofsaess, D. Schlipf, A. Rettenmeier, M. Kuehn... 66 12:15 Discussion 12:30 Lunch VII Wake meandering (first session). ROOM D 14:00 Meandering Wake and Porous Structure Models of Turbulent Wind Fields inside a Wind Farm. David Carruthers, Amy Stidworthy, Julian Hunt, Stephanie Gray……...…… 69 14:15 Status on development and validation of the dynamic wake meandering (DWM) model. T.J. Larsen, H. Aa. Madsen, G.C. Larsen, N. Troldborg, N. Johansen..................... 70 14:30 A tailored eddy viscosity closure consistent with the Dynamic Wake Meandering philosophy. G.C. Larsen, H.Aa. Madsen and N. Troldborg……………………………..… 73 14:45 A quasy 3D computation of multiple wakes using a boundary layer equation BLE model. H.Aa. Madsen, G.C. Larsen, N. Troldborg and T.J. Larsen…………………..…… 75 15:00 Potential load reductions on megawatt turbines exposed to wakes using individual pitch wake compensator and trailing edge flaps. Helen Markou , Peter Bjørn Anderson.… 77 15:30 Coffee Break VIII Wake meandering (second session). ROOM D 16:00 LES-simulation of a turbulent and meandering wake. Thomas Hahm, Steffen Wussow…………………………………………………………….………………………. 78 16:15 Stochastic simulation of wake meander and turbulence in a wind farm. Morten Nielsen………………………………………………………………………………….….. 80 16:30 Wake effects on turbine loading. Laust Olsen, Søren M. Pedersen………………… 81 16:45 Benchmarking of the Risø Dynamic Wake meandering model against CFD-AL calculations. Dick Veldkamp…………………………………………………………….. 82 17:00 Discussion 20:30 Dinner: Paulino de Quevedo, Calle de Jordán nº 7.

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Thursday, 22 October. 10:00 Madrid bus tourist tour in front of the main door of E.T.S.I. Industriales 12:30 Lunch IX Offshore wind farms. Large wind Farms. ROOM MARÍA FERNANDEZ DEL AMO 14:30 ACD modelling of wake interaction in Horns Rev wind farm. Stefan Ivanell, Robert Mikkelsen, Jens N Sørensen, Dan Henningson......................................................... 83 14:45 Modelling the impact of wakes on power output in large offshore wind farms. R.J. Barthelmie, S.T. Frandsen, O. Rathmann, K. Hansen, L.E. Jensen, S.Neckelmann, W. Schlez, J. Philips, K. Rados, J.G. Schepers, E. Politis, J. Prospathopoulos, D. Cabezón….. 84 15:00 A wake flow model for large wind farms in inhomogeneous wind fields. Jochen Cleve………………………………………………………………………………………. 86 15:15 Development of a Large-eddy simulation (LES) model for modelling the far-wake effects of offshore windfarms. G. Steinfeld, S. Raasch, J. Tambke, J. Peinke and D. Heinemann............................................................................................................................. 87 15:30 Modelling Very Large Wind Farms Offshore and Onshore. Wolfgang Schlez, Anja Neubert, Simon Cox............................................................................................................... 90 15:45 Discussion 16:00 Coffe break X Strategies for control based on wind turbine wakes. Fatigue and Loads. Optimization. ROOM MARÍA FERNANDEZ DEL AMO 16:30 A wind farm model in the context of distributed control of the wind farm. Arno J. Brand………………………………………………………………………….……...…….. 91 16:45 Prediction models for wind speed at turbines in a farm with application to control. Torben Knudsen, Mohsen Soltani, Thomas Bak………………………...…….…………... 92 17:00 TOPFARM - A study on Wind Sector Management. Ingemar Carlén…………….. 94 17:15 Wind farm optimization with structured and un-structured grids. Thomas Buhl, Ingemar Carlén and Gunner Larsen………………………………………….…………….. 95 17:30 Discussion 17:45 Closing Address 18:00 End

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SESSIONS

Tuesday, 20 October

8:30 Registration, Welcome + Opening address

I Wake models. Multiple wakes in wind farms. ROOM D9:00 Extensions of the Jensen wake model for wind farm flows Hedevang, E.9:15 Enhanced CFD modeling of wind turbine wakes Prospathopoulos, J.M.9:30 Universal Benchmarks for Wind Turbine Wake and Wind Farm Models Moriarty, P.9:45 Stochastic simulation to study wake meandering using UPMPARK Migoya, E.10:00 Fast linearized models for wind turbine wakes Ott, S.10:15 Discussion

10:30 Coffee Break

II Turbulence closure models. ROOM D11:00 Comparison of turbulence models for the CFD simulation of wind turbine wakes in the AtmosphericCabezón, D.11:15 Energy Preservation in the Numerical Calculation of Wind Turbine Wakes Sanderse, B.11:30 Turbulence closure strategies for modelling wind turbines wake Réthoré, P.E.11:45 Analysis of the wake meandering using a LES method Jiménez, A.12:00 Validation of wake analytical models of WindSim in neutral and stable conditions in a offshore Crasto, G.12:15 Discussion

12:30 Lunch

III Actuator disk and actuator line models. Aerodynamics. Near wake ROOM D14:00 Numerical simulations of wake interaction between two wind turbines at various inflow conditions Troldborg, N.14:15 On actuator disc force fields generating vorticity and wakes Kuik, G.14:30 Meandering Wake Characteristic Derived from Actuator Line Simulations of Wind Turbine Wakes Mikkelsen, R.14:45 Actuator disc momentum theory for low lambda rotors Sørensen, J.N.15:00 Use of actuator disk and actuator surface methods for the aerodynamic modeling of wind turbines: AMasson, C.15:15 Discussion

15:30 Coffee Break

IV Influence of atmospheric stability and topography. ROOM D16:00 The dependence of wake losses on atmospheric stability characteristics Larsen, G.C.16:15 Do wind farms influence large scale turbulence? Larsen, G.C.16:30 RANS simulations of a wind-farm with the application of the actuator disc concept Crasto, G.16:45 Mesoscale and turbulence effects on wind farms Hunt, J.17:00 Numerical simulations of the turbulent logarithmic layer Jiménez, J.17:15 Wind tunnel simulation of the wakes of large wind turbines in off-shore stably stratified flow Pascheke, F.17:30 Large Eddy Simulation study of fully developed wind-turbine array boundary layers Calaf, M.17:45 Discussion

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Wednesday, 21 October

V Experimental work (first session) ROOM D9:00 Comparison and validation of BEM and free wake unsteady panel model with the MEXICO rotor exMicallef, D.9:15 Experimental and numerical investigation of the 3D VAWT wake Ferreira, C.9:30 Development of a process chain for a detailed wake simulation of horizontal axis wind turbines Meister, K.9:45 LiDAR measurements of full scale wind turbine wake characteristics Hansen, K.S.10:00 Decaying Coherent Eddy Structures and Turbulent Fluctuations in Wind Turbine and Wind Farm WSood, A.10:15 Discussion

10:30 Coffee Break

VI Experimental work (second session) ROOM D11:00 Temporal and spatial study of the meandering phenomenon España, G.11:15 Influence of topography and wakes on wind turbulence. Measurements and interpretation of results Jiménez, A.11:30 Advances in wind tunnel testing of wind farm Franchini, S.11:45 Wake measurements of a multi-MW wind turbine with long range lidar Käsler, Y.12:00 Measurements of a multi-MW turbine near-wake using lidar from the nacelle Trujillo, J.J.12:15 Discussion

12:30 Lunch

VII Wake meandering (first session) ROOM D14:00 Meandering Wake and Porous Structure Models of Turbulent Wind Fields inside a Wind Farm Carruthers, D.14:15 Status on development and validation of the dynamic wake meandering (DWM) model Larsen, T.J.14:30 A tailored eddy viscosity closure consistent with the DWM philosophy Larsen, G.C.14:45 A quasy 3D computation of multiple wakes using a boundary layer equation BLE model Madsen, H.Aa.15:00 Potential load reductions on megawatt turbines exposed to wakes using individual pitch wake compeMarkou, H.

15:30 Coffee Break

VIII Wake meandering (second session) ROOM D16:00 LES-simulation of a turbulent and meandering wake Hahm, T.16:15 Stochastic simulation of wake meander and turbulence in a wind farm Nielsen, M.16:30 Wake effects on turbine loading Olsen, L.16:45 Benchmarking of the Risø Dynamic Wake meandering model against CFD-AL calculations Veldkamp, D.17:00 Discussion

20:30 Dinner: Paulino de Quevedo, Calle de Jordán nº 7

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Thursday, 22 October.

10:00 Madrid bus tourist tour in front of the main door of E.T.S.I. Industriales

12:30 Lunch

IX Offshore wind farms. Large wind Farms. ROOM Mª FERNANDEZ DEL AMO14:30 ACD modelling of wake interaction in Horns Rev wind farm Ivanell, S.14:45 Modelling the impact of wakes on power output in large offshore wind farms Barthelmie, R.J.15:00 A wake flow model for large wind farms in inhomogeneous wind fields Cleve, J.15:15 Development of a Large-eddy simulation (LES) model for modelling the far-wake effects of offshor Steinfeld, G.15:30 Modelling Very Large Wind Farms Offshore and Onshore Schlez, W.15:45 Discussion

16:00 Coffe break

X Strategies for control based on wind turbine wakes. Fatigue and Loads. Optimization. ROOM Mª FERNANDEZ DEL AMO16:30 A wind farm model in the context of distributed control of the wind farm Brand, A.J.16:45 Prediction models for wind speed at turbines in a farm with application to control Knudsen, T.17:00 TOPFARM - A study on Wind Sector Management Carlén, I.17:15 Wind farm optimization with structured and un-structured grids Buhl, T.17:30 Discussion

17:45 Closing Address18:00 End

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LIST OF AUTHORS

Name Page Anderson, P.B. ........................................................................................................................ 77 Aubrun, S. ............................................................................................................................... 59 Bak, T. .................................................................................................................................... 92 Bange, J. .................................................................................................................................. 57 Barthelmie, R. ..................................................................................................................... 6, 35 Barthelmie, R.J. ....................................................................................................................... 84 Bischoff, O. ............................................................................................................................. 66 Brand, A.J. .............................................................................................................................. 91 Breton, S.P. ............................................................................................................................. 32 Buhl, T. ................................................................................................................................... 95 Bussel, G.v. ...................................................................................................................... 46, 49 Cabezón, D. ...................................................................................................................... 14, 84 Calaf, M. ................................................................................................................................. 45 Carlén, I. ........................................................................................................................... 94, 95 Carruthers, D. ......................................................................................................................... 69 Castellani, F. ........................................................................................................................... 41 Castellote, F. ........................................................................................................................... 66 Chaviaropoulos, P.K. ................................................................................................................ 3 Cleve, J. ................................................................................................................................... 86 Cox, S. .................................................................................................................................... 90 Crasto, G. .......................................................................................................................... 22, 41 Crespo, A. ............................................................................................................... 8, 14, 20, 61 Cuerva, A. ............................................................................................................................... 62 Devinant, P. ............................................................................................................................ 59 Enevoldsen, K. ....................................................................................................................... 55 España, G. ............................................................................................................................... 59 Esteban, M. ............................................................................................................................. 61 Ferreira, C. ........................................................................................................................ 46, 49 Franchini, S. ............................................................................................................................ 62 Frandsen, S.T. ......................................................................................................................... 84 García, J. ........................................................................................................................... 20, 61 Giménez, D. ............................................................................................................................ 61 Gravdahl, A.R. .................................................................................................................. 22, 41 Gray, S. ................................................................................................................................... 69 Hahm, T. ................................................................................................................................. 78 Hancock, P.E. ......................................................................................................................... 44 Hansen, K. ........................................................................................................................ 55, 84 Hedevang, E. ............................................................................................................................. 1 Heinemann, D. .................................................................................................................. 83, 87 Hofemann, C. ......................................................................................................................... 49 Hofsaess, M. ........................................................................................................................... 66 Hunt, J. ............................................................................................................................. 42, 69 Ighil, T.A. ............................................................................................................................... 38 Ivanell, S. ................................................................................................................................ 83

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Jensen, L. .......................................................................................................................... 35, 84 Jiménez, A. .................................................................................................................... 8, 20, 61 Jiménez, J. ............................................................................................................................... 43 Johansen, N. ............................................................................................................................ 70 Käsler, Y. ................................................................................................................................ 63 Kloosterman, M. ..................................................................................................................... 46 Knudsen, T. ............................................................................................................................. 92 Koren, B. ................................................................................................................................. 16 Krämer, E. ............................................................................................................................... 52 Kuehn, M. ............................................................................................................................... 66 Kuik, G.v. ................................................................................................................... 26, 30, 49 Larsen, G.C. .................................................................................. 23, 35, 38, 55, 70, 73, 75, 95 Larsen, T.J. .................................................................................................................. 35, 70, 75 López, O. ................................................................................................................................ 62 Loyer, S. .................................................................................................................................. 59 Lutz, T. .................................................................................................................................... 52 Madsen, H.Aa. ................................................................................................ 23, 35, 70, 73, 75 Mann, J. ...................................................................................................................... 35, 38, 55 Manuel, F. ................................................................................................................................. 8 Markou, H. .............................................................................................................................. 77 Martí, I. ................................................................................................................................... 14 Masson, C. .............................................................................................................................. 32 Meister, K. .............................................................................................................................. 52 Meneveau, C. .......................................................................................................................... 45 Meyers, J. ................................................................................................................................ 45 Micallef, D. ............................................................................................................................. 46 Migoya, E. .............................................................................................................. 8, 14, 20, 61 Mikkelsen, R. .................................................................................................................... 29, 83 Moriarty, P. ............................................................................................................................... 6 Mouritzen, A.S. ...................................................................................................................... 38 Neckelmann, S. ....................................................................................................................... 84 Neubert, A. .............................................................................................................................. 90 Nielsen, M. .............................................................................................................................. 80 Olsen, L. .................................................................................................................................. 81 Ott, S. ...................................................................................................................................... 11 Øye, S. .................................................................................................................................... 29 Pascheke, F. ............................................................................................................................ 44 Pedersen, S.M. ........................................................................................................................ 81 Peinke, J. ................................................................................................................................. 87 Peña, A. ................................................................................................................................... 35 Philips, J. ................................................................................................................................. 84 Politis, E.S. ......................................................................................................................... 3, 84 Prieto, J.L. ............................................................................................................................... 20 Prospathopoulos, J.M. ........................................................................................................ 3, 84 Raasch, S. ................................................................................................................................ 87 Rados, K.G. ........................................................................................................................ 3, 84 Rahm, S. .................................................................................................................................. 63 Rathmann, O. .......................................................................................................................... 84 Réthoré, P.E. ........................................................................................................................... 19

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Rettenmeier, A. ....................................................................................................................... 66 Sanderse, B. ............................................................................................................................ 16 Sant, T. .................................................................................................................................... 46 Sanz, J. .................................................................................................................................... 14 Schepers, J.G. .......................................................................................................................... 84 Schlez, W. ......................................................................................................................... 84, 90 Schlipf, D. ............................................................................................................................... 66 Sibuet-Watters, C. ................................................................................................................... 32 Simmet, R. .............................................................................................................................. 63 Soltani, M. .............................................................................................................................. 92 Sood, A. .................................................................................................................................. 57 Sørensen, J.N. ............................................................................................................. 29, 30, 83 Sørensen, N.N. ........................................................................................................................ 19 Steinfeld, G. ............................................................................................................................ 87 Stidworthy, A. ......................................................................................................................... 69 Sumner, J. ............................................................................................................................... 32 Tambke, J. ............................................................................................................................... 87 Troldborg, N. ........................................................................................................ 23, 70, 73, 75 Trujillo, J.J. ....................................................................................................................... 63, 66 Veldkamp, D. .......................................................................................................................... 82 Wussow, S. ............................................................................................................................. 78 Zuylen, A.H.v. ........................................................................................................................ 26

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Extensions of the Jensen wake model for wind farm flows

E. Hedevang

Siemens Wind Power A/S, Borupvej 16, 7330 Brande, Denmark, +45 99 42 00 00

Corresponding author E. Hedevang

[email protected] Abstract In previous work by Cleve et al., the engineering wake model of Jensen is used to analyze the wake flow by means two-parameter fits of the model's wake decay parameter and common wind direction. The model performs well provided the data is sufficiently filtered to satisfy the requirements of the model, however, this filtering removes two thirds of the data. Furthermore, other shortcomings of the model where found, and thus the need was identified for further work on generalizations. In this work several such generalizations are investigated and compared. In all of the following cases the wind direction is assumed to be the same at all turbines. The impact of this assumption is investigated by J. Cleve in another contribution to this colloquium. First we consider the potential improvement of extending the wake model from assuming a homogeneous upwind field, that is, that the velocity is the same at the first row of turbines facing the wind, to a heterogeneous upwind field. This extension is of course expected to improve the quality of the fit and the figure below, which shows the distributions of the fit errors, confirms that.

As it takes time for the wind to move from one turbine to the next, we then consider the potential improvement of taking this delay into account, that is, we move from an Eulerian view to a Lagrangean view. We also consider the effect of using shorter time averages than 10 minutes. The effect of taking delay into account will be largest when the velocity of the wind is far from being stationary. In the figure below we compare the distributions of the fit errors of the Eulerian view with the Lagrangean view for 2 minute averages of the data restricted to events where the relative change in farm power from one event to the next is greater than 25% percent, and we observe that the Lagrangean view performs best.

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The difference between the Eulerian view and the Lagrangean view appears to be less pronounced for longer time averages. Another possible extension to the Jensen wake model is to allow different recovery rates for the wakes, that is, different wake decay parameters depending on how far downwind a turbine is placed in the farm. The figure below shows fit of the Jensen model to an event where the wind direction is such that one turbine will be directly in wake of the closest upwind turbine. The fitted wake decay parameters fall in two groups. Except for the group with the high value, which consists of the rearmost rows of turbines relative to the wind direction, the wake decay parameters appear independent of the distance to the upwind park of the farm.

Work is ongoing to include more data into the modelling as it is highly desired to obtain a data set representative of the majority of the wind conditions at the farm. Keywords: wake modelling, Jensen wake model. References Cleve et al., Model-based Analysis of Wake-flow Data in the Nysted Offshore Wind Farm, Wind Energy 2009, 12, 125-135.

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Enhanced CFD Modelling of Wind Turbine Wakes

J.M. Prospathopoulos1, E.S. Politis1, K.G. Rados2, P.K. Chaviaropoulos1

1 Centre of Renewable Energy Sources 19th km Marathonos Ave., 19009, Pikermi, Attiki, Greece

Tel: +302106603300, Fax: +302106603301 2 School of Mechanical Engineering, National Technical University of Athens

9 Heroon Polytechniou, Zografou, Athens

Corresponding Author John Prospathopoulos, e-mail: [email protected]

Abstract Modelling of wind turbine (W/T) wakes using a full 3D Navier–Stokes solver for incompressible flow, along with the k–ω turbulence model suitably modified for atmospheric flows, is presented. The governing equations for incompressible fluid are numerically integrated by means of an implicit pressure correction scheme [1], where W/Ts are modelled as momentum absorbers by means of their thrust coefficient. Apart from neutral, stable atmospheric conditions are also considered. They are modelled by means of an additional buoyancy production (or dissipation) term, which is added to the k and ω equations, without solving a conservation equation for the energy (or the temperature). The flow equations are discretized and solved in their non-dimensional form, using the W/T rotor diameter as a length scale and the free stream wind speed, as a velocity scale. The grid spacing is kept dense around the W/T and close to the ground, and coarsens outwards, following a geometrical progression, until the maximum dimension of the domain is reached. A fine mesh is constructed in the area of the W/T rotor disk, using 20 grid points across the rotor diameter. The numerical model is first applied for the wake simulation of a single wind turbine in flat terrain under neutral and stable atmospheric conditions. The initial (baseline) calculations, however, show a significant underestimation of the near wake deficit compared to the measurements, especially in neutral stratification (Figure 1). The same observation was made by El Kasmi and Masson [2], who attributed the wake deficit underestimation to the existence of a region of non-equilibrium turbulence close to the turbine. They defined that region as a cylindrical volume including the actuator disk and assumed that the region enclosing the rotor disk is characterized by an enhancement of ε when the main strain is strong or when there is a large production rate. That concept along with alternative assumptions are investigated and discussed in order to give a physical interpretation of the delayed flow recovery and suggest a consistent modelling approach for the near wake. The different modelling approaches stem from different physical backgrounds, but they all account for and correct the turbulence overestimation which is responsible for the faster flow recovery appearing in the computations. The second concept considers a decrease in the turbulence decay ratio due to the atmospheric turbulence and the rotor, resulting in a modification of the turbulence model constants. It was proved that these two correction approaches can be tuned to provide satisfactory predictions for the wind speed deficit and the turbulence intensity; however, they require experimental data for calibration of their parameters.

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The third approach sets a bound for the turbulence time scale based on a general “realizability” constraint for the turbulent velocities [5]. This constraint was first suggested to treat the problem of the anomalously large growth of turbulent kinetic energy predicted by the two equation models in stagnation point, aerodynamic flows, but it is general enough and can be extended for any other flow simulation. Although it does not completely correct the wind speed deficit underestimation, it has the advantage of being based on a general constraint and does not need any calibration at all. In Figure 2, the effect of the three approaches is presented for the neutral stratification case of the Nibe experiment.

Figure 1: Single wake wind speed predictions for neutral stratification. Left: Nibe experiment

[3] (Uref= m/s TI=9%). Right: Sexbierum experiment [4]0 (Uref= m/s TI=10%). In stable stratification, the two first corrections result in good prediction of the wake loss at the 2.5D distance; however the wake loss at the 3.5D distance is over-predicted. Durbin’s correction has a smaller influence on the predictions which means that the wake losses are still underestimated.

Figure 2: Single wake wind speed predictions for neutral stratification and TI=9% (Nibe

experiment [3]0). Left: x=2.5D, middle: x=4D, right: x=7.5D. The second issue addressed in this paper concerns multi wake (wind farm) predictions, and specifically the determination of the reference wind speed for the thrust calculation of a turbine located in the wake(s) of other turbines, when the definition of the reference wind speed for the calculation of the thrust is not obvious. This is overcome by utilizing an

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induction-factor based concept: According to it, the definition of the induction factor and its relationship with the thrust coefficient are used to provide an average wind speed value across the rotor disk for the estimation of the axial force. Application is made on the ECN test farm [6]0 of 5 sequential wind turbines comparing the predictions with and without correction for the near wake deficit underestimation (see Figure 3). Predictions underestimate the wake losses, in conformity to the single wake test cases. Comparison of the predicted power ratios with measurements showed that use of Durbin’s constraint resulted first, in partially correcting the initial power underestimation and second, in predicting the small power increase from the second to the fifth turbine, which is in accordance to the experiment.

Figure 3: Predicted power ratios for the ECN test farm with 5 W/Ts in a row. Left: Baseline

calculations. Right: Calculations including Durbin’s correction. 0o correspond to the direction of the row. Measurements are taken from [6]0.

Acknowledgement This work was partly funded by the European Commission and by the Greek Secretariat for Research and Technology under contract SES6 019945 (UpWind Integrated Project). The relevant wind farm owners are acknowledged for supplying the project with data for the model evaluation and ECN for the data processing. Keywords: Wind turbine wakes, CFD modelling, near wake, turbulence model. References [1] Chaviaropoulos, P. K. and Douvikas, D. I., “Mean-flow-field Simulations over Complex Terrain Using a 3D Reynolds Averaged Navier–Stokes Solver,” Proceedings of ECCOMAS ’98, 1998, Vol. I, Part II, pp. 842-848. [2] El Kasmi, A., and Masson, C., “An extended k-ε model for turbulent flow through horizontal axis wind turbines”, J. of Wind Eng. Ind. Aerodyn., 2008, 96, pp.103-122. [3] Taylor, G.J., “Wake measurements on the Nibe Wind Turbines in Denmark”, Contractor Report ETSU WN 5020, National Power – Technology and Environment Centre, 1990. [4] Cleijne, J.W., “Results of the Sexbierum Wind Farm; Single Wake Measurements”, TNO Report No.93-082 for JOUR-0087 project, 1993. [5] Durbin, P.A., “On the k-ε stagnation point anomaly”, Int. J. Heat and Fluid Flow, 1996, 17(1), pp.89-90. [6] Machielse, L.A.H., Eecen, P.J., Korterink, H., van der Pijl, S.P. and Schepers, J.G., “ECN Test Farm Measurements For Validation of Wake Models”, Proceedings of the 2007 European Wind Energy Conference & Exhibition, Milan 7-10/5/2007, Edited by P. K. Chaviaropoulos, pp. 98-102.

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Universal Benchmarks for Wind Turbine Wake and Wind Farm Models

Patrick Moriarty1, Rebecca Barthelmie2

1 National Renewable Energy Laboratory, USA

2 Indiana University, USA Abstract In many fields of computational engineering benchmarks are used to compare models with different physics and authors. The purpose of such benchmarks is to gain insight into the benefits and drawbacks of a set of modeling assumptions for a wide range of applications within a field of study. In wind turbine aerodynamics this has done with the blind comparison to the NREL NASA Ames dataset and will continue under the EU MEXICO project. In atmospheric science, the recent measurements from the Risø Bollund experiment will serve as a benchmark for complex terrain interactions. It is proposed that a similar framework be constructed for models currently being developed for wind turbine wakes and wind farms as a whole. This framework will represent an extension of the work that has been done within Annex 23 to improve wind farm modeling techniques. While Annex 23 was originally limited to offshore wind farms, this new task will focus on all wind farms, both onshore and offshore. The focus will also be limited to the fluid dynamic interactions among wind turbines and with the atmosphere. Much of this new task will involve benchmarking models of wind farms against other models and actual wind farm data. As such, participation by industrial partners willing to openly share wind farm data will be of utmost importance. Benchmarks These benchmarks will involve model intercomparisons and also comparisons to field data. Some benchmarks may exist already, such as various datasets from the Horns Rev wind farm, but some will need to be developed in the coming years. These benchmarks can include, but are not limited to the following: • Model to Model or Theoretical

o Single Wake – how do models compare for a single wind turbine wake? o Multiple Wakes – how do models compare for the case of more than one upstream wake? o Infinite Wind Farm – what is the production from an infinitely large wind farm? Is there and asymptotic relationship between size and production losses? o Stability Classes – what is the impact of atmospheric stability on wind farm production? o Complex Terrain – what is the effect of complex terrain on wind farm production?

• Model to Measurements

o Wind Farm Size – what is the impact of wind farm size on overall production? o Stability Classes – what is the impact of atmospheric stability on wind farm production? o Complex Terrain – what is the effect of complex terrain on wind farm production?

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o Advanced Control Schemes (e.g. ECN’s Heat and Flux) – what control strategies can optimize wind plant performance over a range of operating conditions?

Best Practices As a final result of the framework, participating members will strive to produce a document of best practices for the industry. The practices will cover the wide range of tools currently used by the industry and attempts to quantify the uncertainty bounds for each of the different types of models.

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Stochastic simulation to study wake meandering using UPMPARK

E. Migoya, A. Crespo, A. Jiménez, J. García

Laboratorio de Mecánica de Fluidos, ETSI Industriales, Universidad Politécnica de Madrid

C/ José Gutiérrez Abascal, 2, Madrid 28026, Spain Tel:+34913363152 Fax: +34913363006

Corresponding author

E. Migoya [email protected]

Introduction UPMPARK is a CFD code that describes the diffusion of multiple wakes in the atmospheric surface layer parameterised by Monin-Obukhov scaling, Crespo et al. (1994). The equations describing the flow are the conservation equations of mass, momentum, energy, turbulence kinetic energy, and the dissipation rate of the turbulence kinetic energy. The modelling of the turbulent transport terms is based on the k-ε method for the closure of the turbulent flow equations. This set of equations has been solved numerically using the SIMPLE algorithm. Finite difference methods were used in the discretization of the equations. A parabolic approximation was made and the equations were solved numerically by using an alternate-direction implicit (ADI) method. The developed wake model is three dimensional and pressure variations in the cross-section have to be retained in order to calculate transverse velocities. UPMPARK is less accurate than LES models, but consume less computing time, and can be used, with moderate computing resources to study the behaviour of a whole wind farm. The code has two options; there is a simplified option in which only the convective terms containing the main flow velocity are retained; in the more complicated version the convective terms containing the velocity components perpendicular to the main flow direction are also retained. Formerly, the code was steady, but now UPMPARK retains the non-steady terms, for the simplified version of the code. Unsteady terms have been incorporated considering convection only in the instantaneous flow direction, whose average is in the direction in which the wind turbines are aligned, Figure 1. The equations used to describe the flow are the momentum in the main flow directon, turbulence kinetic energy, and the dissipation rate of the turbulence kinetic energy.

ε,,

...... 000

kVJyJV

xJV

tJJV

tJ

x

yx

=

+∂∂

+∂∂

+∂∂

=+∇+∂∂ r

(1)

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Figure 1: Wind farm scheme.

The program is applied for a wind whose direction changes with time in a sinusoidal fashion. A stochastic simulation, based in Shinozuka (1971), has been implemented to take into account the incident wind variations. Changes in the wind characteristics due to large sale turbulence have been retained and incorporated simultaneously to UPMPARK. Kaimal or Von Karman expression could be employed to obtain spectra in x and y directions. They use as input data the average incident wind direction, the average and variance incident wind speed and the integral scale. Stochastic time series generators are based on the integration of velocity spectrum. Therefore, summations of harmonics, with a random phase and amplitudes which follow the previously mentioned spectral density functions, are used:

yxiktffSfVup

down

jj

jjjjiji ,)2cos()( =+∆= ∑

=

=

π (2)

where t is the time, k is a random phase distributed between 0 and 2π, fj a frequency, between jup and jdown, and ∆fj the distance between frequencies. jup and jdown mean the index of higher and lower filtered scales. The lowest wave length is limited to the wind turbine diameter, D, Equation (3). The incident speed over the wind farm and the misalignment are calculated by Equation (4) and (5) respectively. Figure 2 shows instantaneous profiles for multiple wakes.

1=hub

highest

VDf

(3)

22yxmeandering VVV += (4)

=

y

xVVarctanθ (5)

Distribution of velocity deficitDistribution of velocity deficit

Distribution of kDistribution of k

Figure 2: Instantaneous profiles for multiple wakes.

θ

x direction Vhub=Vcalculation

Vmeandering

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Typical non-linear profiles that show a maximum are expected to be softened because of the meandering effect. Figure 3 compares the averaged results with and without meandering.

Distribution of velocity deficit

Without meandering

Distribution of velocity deficit

Without meandering

Distribution of velocity deficit

Meandering stochastic simulation

Distribution of velocity deficit

Meandering stochastic simulation

Distribution of k

Without meandering

Distribution of k

Without meandering

Distribution of k

Meandering stochastic simulation

Distribution of k

Meandering stochastic simulation

Figure 3: Averaged results with and without meandering for multiple wakes. Keywords: wake meandering, CFD, stochastic simulation, k-ε turbulence closure. References Crespo A., Chacón L., Hernández J., Manuel F., Grau J.C. (1994). UPMPARK: a parabolic 3D code to model wind farms. In: Tsipouridis J. L., editor, European Wind Energy Conference 1994, Thessalonica, Greece, 10-14 October 1994. p. 454- 459. Shinozuka, M. (1971). Simulation of multivariate and multidimensional random processes. The Journal of the Acoustical Society of America, vol. 49, issue 1B, 357-368.

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Fast linearized models for wind turbine wakes

Søren Ott

Wind Energy Division Risø National Laboratory for Sustainable Energy

Technical University of Denmark - DTU P.O. Box 49, DK-4000 Roskilde, Denmark

[email protected]

Corresponding author Søren Ott

[email protected] Abstract Linearized models are known to yield good results in situations where the flow results from a small perturbation. In the case of an offshore wind turbine the unperturbed flow is just flow over a sea surface and the drag exerted by the rotor is the perturbation. Linearization of the problem is therefore a tempting possibility since a linearized model can easily run 1000 times faster than a CFD code, and computational speed is handy when a large number of flow cases are to be studied and/or a large number of turbines are involved. Here we are talking about a linearization of the equations of a particular CFD model. The immediate goal is to mimic the CFD results assuming that these are in reasonable agreement with reality. A perfect match with the underlying CFD model cannot be expected so it is a question of getting as close as possible. There are many ways to do a linearization, and hence many choices to make that can improve it. One of the major problems is that the turbine drag is usually quite large making the flow highly nonlinear in the vicinity of the rotor. On the other hand, linearization is justified in the far field where the perturbation is indeed small.

Figure 1. Normalised velocity deficit in the vertical plane through the hub obtained with a

linearized model. Wind from left to right. Figure 1 shows a fairly well behaved wake. The interfacing with the ground/sea is well handled and the wake in the far field looks ok. However, the wake is generally too weak because the linearized model tends to underestimate momentum transfer and it does not expand the way a real wake would do. In the far field the wake therefore looks as if it was generated by the wrong type of turbine.

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An obvious fix is to use a 'wrong' distribution of the drag forces in order to get the far field wake right. To do this in a rigorous manner we redefine the perturbation problem. Instead of just varying the thrust coefficient, we also vary the rotor diameter in such a way that the expanded wake will tend to keep its diameter fixed. This ensures a close to linear dependence on the induction factor in the far field and restores the correct momentum deficit. We have considered a very simple case: 2D flow past an actuator line with uniform free stream velocity and no turbulent mixing. Figure 2 shows a very good match of centreline velocities and figure 3 shows the approach to the correct width. Further refinements achieved through the use of suitable, curvilinear coordinates is part of ongoing speculations.

5 0 5 10

0.6

0.7

0.8

0.9

xR

UU 0

Figure 2. Centreline velocity in a simple 2D flow past an actuator line. Thick line: ‘exact’,

numerical solution. Thin line: linearized model. Wind is from left to right.

3 2 1 0 1 2 30.40.60.81.01.2

UU 0

3 2 1 0 1 2 30.40.60.81.01.2

UU 0

3 2 1 0 1 2 30.40.60.81.01.2

yR

UU 0

Figure 3. Velocity profiles in a simple 2D flow past an actuator line. Thick line: ‘exact’,

numerical solution. Thin line: linearized model.

x = 2 R

x = 4 R

x = 8 R

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The principle of superposition allows for computational speed through the use of pre-calculated look up tables. It takes some time to generate these tables, but once it has been done they can be used to solve problems with any number of turbines in any configuration. Multiple wakes from many turbines are therefore easy to make and it is easy to move turbine positions or change wind direction. This is because the superposition of the wakes and the (nonlinear) adjustments of the drags are the last steps in the calculation. Figure 4 shows the wake from a whole wind farm consisting of 90 turbines.

Figure 4. The wake from a hypothetical wind farm with 90 turbines.Wind is from left to right. A further advantage is that the equations are formulated in a mixed--spectral setting where there is no computational grid, and hence no numerical diffusion. There are other numerical difficulties arising from solving the two-point boundary value problems and it has been necessary to make a new method to deal with these. Keywords: wind turbine wake, linearized model.

10 km0 km

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Comparison of turbulence models for the CFD simulation of wind turbine wakes in the Atmospheric Boundary Layer

D. Cabezón1, J. Sanz1, I. Martí1, A. Crespo2, E. Migoya2

1 Wind Energy Department, National Renewable Energy Centre (CENER), Spain

2 Departamento de Ingeniería Energética y Fluidomecánica, Escuela Técnica Superior de Ingenieros Industriales, Universidad Politécnica de Madrid (UPM)

Abstract Wake turbine effect has been modelled using different approaches [1][2], from analytical engineering models to 3D CFD full rotor modelling. During the last years and due to the need of modelling wind farms aerodynamics in challenging environments such as complex terrain and offshore, several proposals have come out through the so-called 'back to the basics' concept. An elliptical approach based on coupling the actuator disk technique and numerical CFD modelling can make a fair approximation of the rotor without leaving the main essence of its physics [3]. The model is based on the thrust curve (so that the geometry of the rotor is not considered) and calculates the extraction of axial momentum from the incoming flow at the rotor face by applying a distribution of forces uniformly loaded over it. Using these simplified techniques instead of complete CFD-BEM coupling have demonstrated to have small or even no impact on the axial evolution of the far wake [4], where interference between wakes, turbulence modelling and topographical effects are usually more relevant at estimating power losses due to wake effect. This analysis looks for possible optimum interfaces modeling techniques between the surface boundary layer meteorology as the bounding environment of the wake and rotor aerodynamics. A sensitivity analysis is made for two relevant topics: 1) the meshing topologies, 2) the parameterization of isotropic k-ε turbulence model in its standard and realizable versions as well as an additional approach through the anisotropic model RSM (Reynolds Stress Model). The results obtained from the actuator disk technique will be compared to other wake models such as the parabollic UPMWAKE model [5] and validated using field data from the Sexbierum experiment [6] in order to observe the accuracy on the prediction of wind speed deficit and added turbulence intensity in the wake flow. The results suppose the starting point for getting better adjustments related to the meshing strategy and the turbulence model parameterization in order to simulate rotor wakes in a more efficient way. This task also represents the first stage at the development of future operational releases of the model in order to analyze wake flow in large complex terrain and offshore wind farms. Keywords: Actuator disk, thrust coefficient, turbulence modelling References [1] Vermeer L.J., Sorensen J.N., Crespo A., 2003, Wind turbine wake aerodynamics. Prog.

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A.S. 39, 467-510 [2] Barthelmie, R.J., Frandsen, S.T., Rathmann, O., Politis, E., Prospathopoulos, J., Rados, K., Hansen, K., Cabezon, D., Schlez, W., Phillips, J., Neubert, A., van der Pijl, S. and Schepers, G. 2008: Flow and wakes in large wind farms in complex terrain and offshore. European Wind Energy Association Conference, Brussels, March 2008 (Scientific track) [3] Crespo A., Manuel F. and Hernández J., "Numerical modelling of wind turbine wakes", Proceedings of European Community Wind Energy Conference pp 166-170 (1990), Madrid (Spain), H.S. Stephens & Associates [4] El Kasmin A., Masson C., An extended k- model for turbulent flow through horizontal-axis wind turbines, J. Wind Engineering and Industrial Aerodynamics 96 (2008), 103-122 [5] Crespo A., Hernandez J. et. al. Experimental validation of the UPM computer code to calculate wind turbine wakes and comparison with other models, J. Wind Engineering and Industrial Aerodynamics 27 (1988), 77-88 [6] Cleijne J.W., Results of Sexbierum Wind Farm, Report MT-TNO Apeldoorn 92.388, 1992

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Energy Preservation in the Numerical Calculation of Wind Turbine Wakes

B. Sanderse1, 2, B. Koren2

1 ECN, Energy Research Centre of the Netherlands Westerduinweg 3, 1755 ZG Petten, The Netherlands

2 CWI, Dutch Centre for Mathematics and Computer Science

Corresponding author B. Sanderse

[email protected] Introduction In order to calculate the wakes of wind turbines and their interaction in wind farms, the current state of the art is to solve the incompressible Navier-Stokes equations with a suitable turbulence model (e.g. a RANS or LES model), and with an actuator-type approximation of the wind turbine blades [5]. Especially in LES it is important that the numerical scheme used not only conserves first-order quantities as momentum but also second order quantities like kinetic energy [3]. The method of Harlow and Welch [1] posesses this property through the use of staggered grids, and has been used in so-called symmetry-preserving discretizations [7]. In such discretizations, sometimes called mimetic, the difference operators mimick the properties of the underlying differential operators. In this way the discrete kinetic energy can only change due to viscous dissipation, leading to a discretization that is stable on any grid. Preliminary results We have tested a second-order symmetry-preserving discretization [7] in two and three dimensions for actuator-type simulations. The equations under consideration are the incompressible Navier-Stokes equations: 0=⋅∇ ur (1)

fupuutu rrrrr

+∇+−∇=∇⋅+∂∂ 2

Re1)( . (2)

The body force fr

is related to TC , the thrust coefficient of the rotor. For lightly loaded actuator discs ( 1<<TC ) in two-dimensional inviscid flow an analytical solution is available that is used to test our discretization:

,tantan2

11

+

+

−∆

= −−

xyR

xyRpp

π (3)

.

wake

up

upuu

∞∞∞

∆−−=ρρ

(4)

The use of a staggered grid not only leads to kinetic energy conservation, but also facilitates the inclusion of the body force, without resorting to the Rhie-Chow interpolation necessary in colocated discretizations [4]. Figures (1) and (2) show the velocity and pressure field for a simulation at 1000Re = and

01.0=TC , performed with the grid shown in figure (3). On the left side of the domain, inflow conditions are prescribed; the pressure is prescribed on all other sides (outflow). With such

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conditions the wake can expand and fluid can flow through the upper and lower sides of the domain.

In figures 4-7 the numerical solution is compared to the analytical solution. When the Reynolds number attains a certain minimum value (here 1000Re ≈ ) the wake behaviour is essentially inviscid and can be compared to the analytical solution. In all figures it is observed that the correspondence between the numerical solution and the analytical solution is perfect, including discontinuities in pressure (figure 4) and velocity (figure 7). The behaviour of the pressure is in general insensitive to Reynolds number.

Figure 1: Pressure contours Figure 2: Velocity contours

Figure 3: Grid. Every fourth grid line is shown.

Figure 4: Pressure through the centerline of the disc Figure 5: Velocity through the centerline of the disc

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Ongoing and future work The ideas of symmetry preservation and conservation are currently pursued in extending the method to three-dimensional turbulent flow. The fourth order discretization of Veldman and Verstappen [7] will be used, in order to avoid interference with the sub-grid scale model [2]. Instead of adapting the diffusive operator of the Navier-Stokes equations, as done in RANS computations, in our opinion it is more logical to model turbulence through approximations of the non-linear convective term. This term is responsible for transferring energy from large to small scales of the flow. Convection-operator based turbulence models are then constructed such that the symmetry and conservation properties are preserved [6]. Keywords: CFD, energy conservation, staggered grid, mimetic, symmetry preservation References [1] F.H. Harlow and J.E. Welch. Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface. Physics of Fluids, 8:2182–9, 1965. [2] A.G. Kravchenko and P. Moin. On the effect of numerical errors in large eddy simulations of turbulent flows. Journal of Computional Physics, 131:310–322, 1997. [3] K. Mahesh, G. Constantinescu, and P. Moin. A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics, 197:215–240, 2004. [4] P.-E. Réthoré and N.N. Sørensen. Actuator disc model using a modified Rhie-Chow/SIMPLE pressure correction algorithm. Comparison with analytical solutions. In European Wind Energy Conference, Brussels, 2008. [5] B. Sanderse. Aerodynamics of wind turbine wakes. Technical Report ECN-E–09-016, Energy Research Centre of the Netherlands, 2009. http://www.ecn.nl/publications/default.aspx?nr=ECN-E--09-016. [6] R. Verstappen. On restraining the production of small scales of motion in a turbulent channel flow. Computers & Fluids, 37:887–897, 2008. [7] R.W.C.P. Verstappen and A.E.P. Veldman. Symmetry-preserving discretization of turbulent flow. Journal of Computational Physics, 187:343–368, 2003.

Figure 6: Pressure across the wake at x=1 Figure 7: Velocity across the wake at x=1

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Turbulence closure strategies for modelling wind turbines wake

Pierre-Elouan Réthoré, Niels N Sørensen.

Risø National Laboratory, Roskilde, DK-4000, Denmark

Corresponding author Pierre-Elouan Réthoré

[email protected] Abstract With the price of supercomputers decreasing, modelling wind turbines and wind farms wake using CFD methods is now close to be an alternative to the faster engineering models. It is now relatively cheap to carry on steady-state computations of wind turbines modelled as actuator discs in atmospheric flows using the RANS methods. By using such methods, the scales of wind turbine wake turbulence is modelled at the same time as the scales of atmospheric turbulence. The RANS methods are by principle modelling all the scales of turbulence together, by estimating an equivalent length scale and velocity scale. These two scales are combined to form the eddy viscosity concept. The Reynolds stress are then estimated using this eddy viscosity and the local wind speed gradient using the so-called Boussinesq approximation. This way of modelling wind turbine wake turbulence was found to be unrealistic by several recent publications (e.g. El Kasmi and Masson (2008), Réthoré and Sørensen (2009), Cabezon et al. (2009), Rados et al. (2009)). These articles postulated that the problem is caused by how the two scales of turbulence are modeled. The present work demonstrates that the type of flow considered is outside the envelop of the Boussinesq approximation assumptions. The Boussinesq approximation is based on an analogy between the molecular and the turbulence momentum transport phenomena. In order to model the Reynolds stress using the local flow information, some drastic assumptions are made over the behaviour of the flow in the surrounding area encompassed by the turbulence length scale (e.g. linearity, conservation of momentum). By introducing the wind turbine in the atmospheric boundary layer turbulence, the flow violate the assumptions of the Boussinesq approximation. The turbulence length scale remains very large, but the changes of the flow are occuring over relatively smaller scales. The net effect of the break down of these assumptions is that the Reynolds stress are largely overestimated both upstream and downstream the wind turbine, leading to an unrealistically high wake dissipation. The present work is addressing this issue by presenting several strategies to cope with the Boussinesq approximation limitations.

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Analysis of the wake meandering using a LES method

A. Jiménez, E. Migoya, J. García, A. Crespo, J.L. Prieto

Laboratorio de Mecánica de Fluidos Escuela Técnica Superior de Ingenieros Industriales, Universidad Politécnica de Madrid

C/ José Gutiérrez Abascal, 2, Madrid 28026, Spain Tel:+34913363152, Fax: +34913363006

Corresponding author

A. Jiménez [email protected]

Abstract A LES model with simplified wind boundary conditions has been used recently to simulate and characterize the turbulence generated by the presence of a wind turbine and its evolution downstream the machine. Important characteristics of the turbulent flow, as velocity defects and turbulence intensity increase in the wake, have been satisfactorily predicted by this methodology. Unfortunately, the meandering of the wake that is supposed to be induced by the presence of big eddies in the free stream sweeping the whole wake away to one side and to the other, has not been detected with the previous calculations. This is probably due to the sub estimation of the energy spectral density in the lowest frequencies of spectrum, which are related with the large scale turbulence responsible of wake meandering. Previous analysis of the wake carried out with the wind turbine placed with a yaw angle related to the main flow direction show an initial skew angle of the wake and a deflection of the centre line trajectory downstream. If the yaw angle is changed dynamically inducing an oscillation into a range of values with the suitable parameters, the real flow seen by the wind turbine will be enriched in large scale turbulent fluctuations, compensating the previous lack of energy in these scales, and introducing a wake meandering that is characterized in the present study. Another aspect of interest is the possible influence the computation domain size (in streamwise, spanwise and vertical direction) on the wake meandering characteristics, due to the periodic boundary conditions used in the LES computations carried out. Attempts have been done in order to detect, clarify and estimate the magnitude of this influence. These approaches to wake meandering analysis are being used to validate a pseudo-steady calculation procedure with less time-consuming models based on RANS calculation, as UPMWAKE and UPMPARK, which use a k-ε closure method, and to estimate the value of the limiting frequency below which both approaches give similar results. References: Crespo, A. and Hernández, J., 1989. Numerical Modelling of the Flow Field in a Wind Turbine Wake. The American Society of Mechanical Engineers, Forum on Turbulent Flows, ASME FED, 76, 121−129. Crespo, A., Hernández, J. and Frandsen S., 1999. A Survey of Modelling Methods for Wind-Turbine Wakes and Wind Farms. Wind Energy, 2, 1, 1 24.

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Jiménez, A., Crespo, A., Migota, E. and García, J., 2007. Advances in large-eddy simulation of a wind turbine wake. Journal of Physics: Conference Series, 75, 012041. Jiménez, A., Crespo, A., Migota, E. and García, J., 2008. Large-eddy simulation of spectral coherence in a wind turbine wake. Environ. Res. Lett., 3, 015004. Parkin, P., Holm, R. and Medici, D., 2001. The application of PIV to the wake of a wind turbine in yaw. Proc. 4th International Symposium on particle image Velocimetry, Göttingen.

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Validation of wake analytical models of WindSim in neutral and stable conditions in a offshore.

Giorgio Crasto, Arne Reidar Gravdahl

Corresponding author Giorgio Crasto, Ph.D.

Software Developer, WindSim AS, c/o Studio Rinnovabili, Via Lagrange, 1 - 00197 Roma

Tel +39 06 8073469 Fax+39 06 80693106 www.windsim.com

Abstract Three analytical wake models for single wakes are tested in the CFD software WindSim for simulations in neutral and stable conditions. RANS simulations of the Atmospheric Boundary Layer are first performed over the sea; the turbulence is closed with the standard k-e model. The analytical models for the wakes are applied to filter the results of the CFD simulations by providing wind deficit and additional turbulence. Superposition of wakes is also modeled by taking into account several approaches. Comparisons are performed against production data of an offshore wind park.

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Numerical Simulations of Wake Interaction between Two Wind Turbines at Various Inflow Conditions

N. Troldborg, G.C. Larsen, H.A. Madsen

Wind Energy Department, Risø DTU National Laboratory for Sustainable Energy, DK-4000

Roskilde, Denmark

Corresponding author N. Troldborg

[email protected] Objectives The objective of the present work is to study the effect of wake interaction between two wind turbines using the so-called actuator line method [1]. Results are presented for varying mutual distances between the two turbines and both full wake as well as half wake situations is considered. Furthermore, simulations are carried out at two different atmospheric turbulence intensities representing onshore and offshore conditions, respectively. From the simulations the main characteristics of the interacting wakes are extracted including the averaged velocity and the turbulence field. The results from the simulations will be used as a basis for calibrating the dynamic wake meandering (DWM) engineering model [2]. Prior work Although being a subject of many investigations the overall behavior of interacting wind turbine wakes is complex and still not well understood. Most field studies on wake interaction [3, 4] rely on nacelle and/or met masts anemometry measurements of the flow field along as well as instruments for measuring structural loading. More recently, the effect of wake interaction was also studied by Madsen et al. [5] using a pitot tube mounted on the blade of a full scale turbine. A common difficulty of these studies is that the few measuring stations provide only limited information about the full flow field which, combined with the ever changing inflow conditions occurring in the field, make it difficult to identify the effect of a specific process. However, some of these limitations are expected to be greatly reduced in a series of comprehensive measurements recently planned within the DAN-Aero experiment and the TOPFARM project. Several of these experiments are already in full progress and aims at bridging the gap between the different flow regimes ranging from blade aerodynamics over rotor and wake aerodynamics to the characteristics of the atmospheric boundary layer. As reviewed in [6], several authors used wind tunnel experiment to study wake interaction in wind farms consisting of small model wind turbines or actuators. Even though such studies can provide useful information about some main features of the wake structure they are often put at a disadvantage due to low Reynolds numbers and other scale effects. Wake interaction has also been investigated extensively using CFD combined with actuator disk/line based methods for modelling the rotors. The majority of these consider rows of

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turbines at different inflow conditions [7-8], but also some have been conducted on entire wind farms [9] including Horns Reef’s wind farm. Generally, the advantage of using numerical methods is that they besides providing all necessary information about the wake also makes it easier to study the effect of changing a single parameter. Nevertheless, there is still a clear need for studying wake interaction in a more systematic manner in order to provide a more complete and general picture of its nature. A partial intention of the present work is therefore to contribute to the overall understanding of the behaviour of interacting wakes. Approach The numerical simulations of the two wind turbines are conducted using the actuator line method [1]. The basic idea of this method is to combine a three-dimensional Navier-Stokes solver with an actuator line technique, in which body forces are distributed along lines representing the blades of the wind turbine. Thereby, the flow field is governed by full three-dimensional Navier-Stokes simulations using LES, whereas the loads on each blade are determined from an aerodynamic model using the local angle of attack and tabulated airfoil data. The main advantage of the method is that the presence of the rotor is modeled without having to resolve the viscous airfoil boundary layer, and therefore the grid resolution can be significantly reduced compared to full CFD. For this reason the method allows for detailed studies of the wake region while still keeping the number of grid points at a reasonable level. The atmospheric boundary layer is modeled using a technique [10] where body forces, applied to the entire computational domain, are used to impose a given, but arbitrary, steady wind shear profile, while free-stream turbulence is modeled by introducing synthetic turbulent velocity fluctuations to the mean flow in a predefined cross-section upstream of the rotor [7]. Results Figure 1 display contours of the instantaneous vorticity in a horizontal plane through the centre axis of the rotors in respectively a full wake and a half wake situation. In both cases the turbulence intensity is around 10% while the mean inflow velocity is given by a power law profile:

α

= ∞ H

yVyV )(

Here y denotes the height above ground, V∞ = 8 m/s is the mean wind speed at hub height, H=1.4R and α = 0.2. In both cases the ambient turbulence causes the wake of the upstream turbine to break up prior to impacting the second rotor. However, it is evident that the downstream turbine experiences very different flow conditions in the two cases: When the mean wind is aligned with the rotors the downstream turbine is fully immersed in the wake from the upstream turbine and hence operates in a flow field characterized by broad band turbulence. In the half wake situation, on the other hand, the downstream turbine experiences a highly inhomogeneous flow field by as the blades rotates in and out of the upstream wake.

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a)

b) Figure 1: Instantaneous vorticity contours of flow field in a horizontal plane located at hub height. The mean wind is coming from the left and the wind turbines are indicated as black

lines. Regions of high vorticity appear as light colors. a) Full wake; b) Half wake. Key words: Wind turbine wakes interaction, actuator line, large eddy simulation, atmospheric boundary layer. References [1] Sørensen, JN. and Shen, WZ. (2002). Numerical modelling of Wind Turbine Wakes. Journal of Fluids Engineering, Vol. 124, Issue 2. [2] Larsen, GC. et al. (2008) Wake Meandering - A pragmatic Approach. Wind Energy, Vol. 11 [3] Højstrup, J. et al. (1993) Full-scale measurements in wind turbine arrays. Nørrekær Enge II. CEC/Joule. Risø report I684. [4] Barthelmie, RJ. et al. (1994) The Vindeby project: a description, Risø-R-741(EN), Roskilde, Denmark [5] Madsen, HA. et al. (2005) Wake flow characteristics in low ambient turbulence conditions. Copenhagen Offshore Wind, Copenhagen, Denmark. [6] Vermeer, LJ. et al. (2003) Wind Turbine Wake Aerodynamics. Prog. in Aerospace Sciences, Vol. 39 [7] Troldborg, N. (2008) Actuator Line Modeling of Wind Turbine Wakes. PhD thesis, Technical University of Denmark. [8] Mikkelsen, R. et al. (2007) Analysis of Power Enhancement for a Row of Wind Turbines Using the Actuator Line Technique. J. of Physics: Conf. Series. TWIND. [9] Ivanell, S. (2009) Numerical Computation of Wind Turbine Wakes. PhD thesis, Royal Institute of Technology, Stockholm, Gotland University, Sweden. [10] Mikkelsen, R. et al. (2007) Prescribed Wind Shear Modelling Combined with the Actuator Line Technique. EWEC, Milan.

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On actuator disc force fields generating wake vorticity

GA.M. van Kuik, A.H. van Zuylen

Duwind - Technical University Delft, Faculty of Aerospace Engineering, Kluyverweg 1, 2629HS Delft, the Netherlands, tel. +31152785170

Corresponding author:

Gijs van Kuik, [email protected]

1 Introduction: Actuator disc calculations can be divided in two categories: force models where, for a prescribed force field, the flow is calculated using a CFD method, and kinematic models, where the wake is calculated based on wake boundary conditions and the force field is known when the velocities are known. In both categories, but specifically for the kinematical models, results are reported that differ some 10% from momentum models. Furthermore, most calculations which give details about the flow through the disc do not satisfy the condition derived by Xyros & Xyros (2007) that the axial velocity through the disc is uniform for discs with a uniform surface load. Apart from this, the inconsistency in the momentum models discussed by van Kuik (2003) is still unresolved. These observations raise the questions: what is the relation between force- and flow field, what are the requirements for a steady axisymmetric force field to generate vorticity in an Euler flow? 2 The equations of motion: A new formulation for the equation of motion for actuator disc flow fields is obtained by merging of three equations: the Euler equation of motion, H ρ= ∇ − ×f v ω (1) the power conversion equation rfϕ⋅ = Ωf v (2) which equates torque times rotational speed to the work done by the force field, and the expression for axisymmetric vorticity ω in a cylindrical system (x,r,φ). This results in: ( rotρ= − ×f v ω )2rot rot x+ × Ωv e (3) rotρ= − ×v ω (4) where the transformation from the co-rotating reference frame to the inertial frame is v rot= v - eφΩr and ωrot = ω - ex2Ω, e being the unit vector. The first term at the right hand side of (3) is the Kutta-Joukowsky force on the bound vorticity, where the second term is the Coriolis force. Both are perpendicular to the local velocity, so do not perform work in the rotating system. In eq. (4) the subscript rot distinguishes this expression from the expression of a Kutta-Joukowsky force. Compared to Euler equation (1) the Bernoulli constant H is absent since the conversion of power is now expressed in kinematical terms. This enables a much easier interpretation of the flow and force field, and makes a comparison possible of the disc force and flow field with the force and flow field of real rotor blade, see section 4. Eq. (4) is consistent with Wu (1962), who derived the flow equation expressed in the streamfunction, showing the occurrence of a force component perpendicular to the streamtube. According to (4) this is the load on disc-bound vorticity.

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3 The generation of a Rankine vortex The new formulation of the actuator disc force field is confirmed by an analytical, exact, solution: the generation of a Rankine vortex by a force field in a flow that is irrotational upstream of the disc. The disc has thickness ε. The vorticity that is generated in the vortex kernel (radius R) is axial, see figure 1. Eq. (4) gives the force field, showing axial and azimuthal components as expected. For r < R, so where vorticity is produced, also a radial component is present. Interpretation of this component in the inertial frame shows that it is needed to satisfy the centripetal momentum balance in the disc volume. In the rotating system it is the Kutta-Joukowsky and Coriolis force acting on the bound vorticity. The impact of this load is verified by numerical calculations using Fluent. For a thick disc, ε = R, figure 2 shows the radial velocity. Indeed application of only the appropriate thrust and torque is not sufficient. For a thin disc the effect of the absence of a radial force vanishes, as confirmed by the analytical solution.

4 The force field of a rotor blade Before discussing the classical disc with uniform axial surface load, the correspondence between a disc- and a rotor force field is treated. Although eq. (4) is derived for the disc, is also the equation used to determine blade loads. This is usually done in the rotating reference frame, applying the Kutta-Joukowsky law L = -ρ v rot x Гrot , where Г = ∫ωdC is the circulation bound in the blade cross section C. Since ωrot= ω - e x2Ω, only the axial component of Γ is affected by the transformation rotating-to-inertial. For blades with a zero pitch angle, Γ x = 0 so Γ rot ≡ Γ . Then the blade load is L = -ρ v rot x Г which is the integrated version of (4). Figure 3 shows a rotor blade vortex system, including the

Figure 2: the radial velocity for a disc force field without radial fr. Note that ε = R.

Figure 1: Generation of a Rankine

Figure 3: blade vorticity and

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loads given by (4). At the tip, bound azimuthal vortic-ity exists, carrying a normal and spanwise load when v rot ≠ 0. The normal tip load is known as the lift on the bound part of the tip vortex. A discussion on the occurrence of in-plane loads is found in Milne-Thomson (1966) §10.61. Now for two wing flows the spanwise load is determined using Kutta-Joukowsky’s expression. For the elliptic wing it is proportional, like the induced drag, to Г2

max/A (A is aspect ratio, Гmax at mid-span) and for Prandtl’s horseshoe vortex to Г2/b (b is the span). In general it is shown that the spanwise load is equivalent to the pressure integrated on the spanwise-projected surface. The conclusion is that finite lifting surfaces, like rotor blades, carry a span-wise load. For wings this load is always neglected. The question is whether this is also allowable for rotors or actuator discs. 5 The classical actuator disc For the flow case with only azimuthal vorticity ωφ (no tor-que, no swirl) there is no analytical solution available to check the possible impact of the load on the bound vorticity. All results published in literature do not account for fedge , except Greenberg & Powers (1970). For e.g. the ‘hover’ disc they have published analytical results including a singularity in ωφ at the disc edge. The results deviate 10% from momentum theory results, which they could not explain. When the force at the singularity is calculated and included in the momen-tum balance, the results agree. CFD calculations show that without applying an edge force similar results as reported in Sörensen e.a. (1998) are obtained. Calculations including the edge load derived from Greenberg & Powers are ongoing. 6 Conclusions The disc force field cannot be chosen arbitrarily, as shown by the force field generating a

Rankine vortex. The load on disc-bound vorticity has to be included. For the classical actuator disc the radial component hereof corresponds to the radial load

on a real blade, which is non-zero. One result reported in literature implicitly accounts for the load on the disc-bound

vorticity. Accounting for this load in momentum theory gives agreement with the results, whereas the authors observed disagreement.

Keywords: actuator disc, force field, vorticity, wake References Greenberg, M.D, Powers, S.R., 1970, Non-linear actuator disk theory and flow field calculations including non-uniform loading, NASA-CR-1672 Kuik, G.A.M. van, 2003, An inconsistency in the actuator disc momentum theory, Wind Energy 7, 9-19. Milne-Thomson, L.M., 1966, Theoretical Aerodynamics, 4th edition, MacMillan and Company Ltd, reprinted in 1973 by Dover Publications, New York. Sörensen J.N., Shen, W.Z., Munduate, X., 1998, Analysis of Wake States by a full-field Actuator Disc Model, Wind Energy 1, 73-88. Wu, T.Y., 1962, Flow through a heavily loaded actuator disc, Schiffstechnik, 9, 47 Xyros, M.I., Xyros, N.I., 2007, Remarks on wind turbine power absorption increase by including the axial force due to the radial pressure gradient in the general momentum theory, Wind Energy, 10, 99.

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Meandering Wake Characteristic Derived from Actuator Line Simulations of Wind Turbine Wakes

Robert Mikkelsen, Jens N. Sørensen, Stig Øye

Department of Mechanical Engineering, Fluid Mechanics Section, Build. 403,

Technical University of Denmark, 2800 Lyngby

Corresponding author Robert Mikkelsen

Department of Mechanical Engineering, Fluid Mechanics Section, Building 403 Technical University of Denmark, 2800 Lyngby

Phone: +4545254320 [email protected]

Abstract The wake meandering characteristics are analyzed from simulated CFD wakes using the actuator line technique combined with the EllipSys3D flow solver. Aerodynamic and aeroelastic loads are handled combining EllipSys3D with the FLEX5 structural code. Simulations a carried out in a turbulent, sheared wind field at a number of wind speeds. The trailed and shed vorticies from the actuator line forming the wake are analyzed at a number of downstream positions. Wake center is derived considering the center of gravity of the turbulent deficit as a representative measure. Thus, the turbulent wake deficits are quantified with respect to magnitude, center position, shape and turbulent content. Various types of Gaussian fits at these locations are tested. Results are shown from single wake simulation and a row of turbines exposed to full wake.

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Actuator disc momentum theory for low lambda rotors

Jens Nørkær Sørensen1, Gijs van Kuik2

1 Technical University of Denmark, [email protected] 2 Duwind, Technical University Delft, [email protected]

Abstract The Blade Element Momentum theory is based on the work of Glauert who formulated the equations to derive thrust, torque and power as a function of the tip speed ratio λ and axial induction. The moment of momentum applied to the wake, is taken into account in his theory with one major simplification. The radial pressure distribution required to maintain the swirl in the wake is ignored, and not included in the momentum balance and the final results. For high λ the swirl is negligible so this simplification has no effect, but for low λ this is questionable. After Glauert, many authors have published solutions for the low λ regime of discs with constant circulation, all with different assumptions on the radial distribution of flow quantities, the momentum balance or the impact of the infinite pressure in case of a discrete vortex at the disc axis. A common property of the results is that the power coefficient Cp increases above the Lanchester-Betz-Joukowsky limit. As for most other authors, the present analysis proceeds from actuator discs with constant circulation, yielding a wake flow characterized by a singular vortex at the downstream disc axis. Without any further assumption, the impact of the radial pressure distribution on the momentum balance and the Bernoulli equation is taken into account, as is the effect of the infinite pressure at the disc axis due to the discrete vortex. The results are presented in analytical expressions for the axial and azimuthal velocities through the disc and in the far wake, and similarly for the thrust, power and torque. The inclusion of the pressure-due-to-swirl gives Vaxial-disc > 0.5(Vwake+Vundisturbed) and the maximum power coefficient indeed tends to infinity for λ→0. Furthermore, the maximum Cp-value is always greater than the Lanchester-Betz-Joukowsky limit at 16/27. The explanation for this is that the axial velocity through the disc becomes larger than the undisturbed velocity: air at a radial distance that is larger than the disc radius is sucked through the disc due to the under-pressure induced by the swirl. This behavior has been the subject of many considerations and explanations. Glauert (1935) stated that the condition of constant circulation cannot be fully realized in practice since it implies that near the roots of the blades the angular velocity imparted to the air is greater than the angular velocity of the propeller itself. Other investigators, such as de Vries (1979) and Wilson and Lissaman (1978), dealt the view point of Glauert that the solution is unphysical as it results in infinite values of power and circulation when the tip speed ratio tends to zero. In a recent work, Sharpe (2004) argues that the theory in principle establishes that there is no loss of efficiency associated with the rotating wake and that it is possible, at least in theory, to exceed the Lanchester-Betz-Joukowsky limit. Thus, still today, there seems not be fully agreement in the validity of the model.

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In the present work we have investigated the basic assumptions and equations leading to the high Cp-values. As a result we found that it most likely is the use of the axial momentum equation that is causing the very high increase in Cp. This equation is used in the limit where Re→∞ which means that friction on the lateral boundary of the control volume is ignored. In the present analysis we include a lateral force term in the formulation of the axial momentum equations. The problem is that the force term is not known a priori, which is also is the reason that it usually is neglected in the momentum analysis. Although we do not know the exact expression; it must be proportional to the area expansion and the pressure drop over the rotor. Thus, we propose to model it using a proportionality factor, denoted ε, which then is introduced as an additional variable in the system of equations. A remarkable result of the analysis is that for all ε-values the power coefficient becomes zero at zero tip speed ratio. Even utilizing as small ε-values as 10-7, the power coefficient becomes exactly zero for λ→0, and for ε≤0.1 Cp is always lower than the Lanchester-Betz-Joukowsky limit. This tells us that one has to be very careful when using the momentum equation, since it generally contains terms that are unknown and that may have a large impact on the final result in the limit of the model. As an alternative we propose a model with constant circulation in which we neglect expansion. In this case we avoid the use of the momentum equation and as a result we get a Cp-distribution that is larger than the one obtained by Glauert and which, in accordance with physical and practical intuition, never exceeds the Lanchester-Betz-Joukowsky limit. References 1. Glauert, H. (1935) “Airplane Propellers”. Division L in Aerodynamic Theory, vol. IV, Durand WF (ed.). Springer: Berlin, pp. 169–360. 2. Vries, O. de (1979) “Fluid dynamic aspects of wind energy conversion”. AGARD Report AG-243. 3. Wilson, R.E. and Lissaman, P.B.S. (1974) “Applied Aerodynamic Performance of Wind Power Machine”s. Oregon State University: Corvallis, OR. 4. Sharpe, D. (2004) “A General Momentum Theory Applied to an Energy-extracting Actuator Disc”. Wind Energy, vol. 7, pp 177-188.

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Use of actuator disk and actuator surface methods for the aerodynamic modeling of wind turbines: A review

Christian Masson*, Christophe Sibuet-Watters+, Simon-Philippe Breton*, Jonathon Sumner*

*Ecole de technologie supérieure,Montréal, Canada. +CENER, Pamplona, Spain.

Corresponding author [email protected]

Abstract A review of the works completed by the research group of Professor Christian Masson over the past ten years related to the use of actuator disk and actuator surface concepts to model the aerodynamic action of a wind turbine (WT) within CFD methods is presented. First, flow and rotor models are discussed. The most important findings are then reviewed. 1 Flow Modelling The following equations constitute the framework for a URANS analysis of the flow aerodynamics in the vicinity of WTs. They integrate the effects of unsteadiness, turbulence and the turbine rotor. They are presented in integral form for a control volume V being delimited by an outer surface A, itself oriented by a normal unit vector ni . ui , p and T refer to the flow velocity, pressure and temperature, respectively, while k and ε are the turbulent kinetic energy and its rate of dissipation. The flow is considered incompressible with density ρ; the Boussinesq approximation is used to account for buoyancy.

In these equations, D*/Dt is the total derivative with respect to time, di,j the Kronecker delta, ti,j the viscous-stress tensor (including Reynolds stresses), mt the turbulent viscosity, Cp the dry air specific heat at constant pressure, gi the acceleration due to gravity, and σT the turbulent Prandtl number. Cµ, Cε1 , Cε2 , Cε3 , σε and σk are constants of the k-ε model whose standard values must be adapted for atmospheric boundary layer flows. Regarding the specific term for buoyancy (highlighted as ), an expression is derived in Ref. [2] for the constant Cε3 as a function of the Monin-Obukhov length to ensure that the Monin-Obukhov relations for atmospheric flows under various stability conditions are exact solutions of the above system of equations for horizontally-homogeneous terrain. Ref. [1] has recently proposed the use of source term in the dissipation equation (5) to increase the energy transfer rate from large-scale turbulence to small-scale turbulence. This term acts within a volume VROTOR , defined as the region of non-equilibrium turbulence around the rotor which

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takes the shape of a cylindrical volume extending approximately 0.25D upstream and downstream of the rotor. 2 Rotor Modelling In the momentum equation (2), the term Fi (highlighted with the symbol ) refers to the external forces exerted on the flow by the WT, tower or nacelle. Refs. [4, 5] discuss the introduction of tower and nacelle effects. The actuator disk (AD) or actuator surface (AS) concepts are used to model the WT action. A detailed description of these concepts and their implementation within a CFD method can be found in Ref. [7]. Here, we review their most important theoretical characteristics. An AD (or an AS) models the blade-bound vorticity using porous surfaces of shape similar to the modeled object (a cone in the case of an AD modelling the WT rotor - or a disk providing zero angle of conicity ; rotating planar surfaces in the case of an AS modelling the individual WT blades). These porous surfaces are the locus of velocity and pressure discontinuities. The mathematical description of the AD/AS object is made easier by considering that these surfaces are vortex sheets whose magnitude can be described by a vorticity vector γ that measures the integral value of vorticity over the sheets. γ(x,y,z) is a Dirac-type function and has units of vorticity x distance. A particle of fluid that crosses an AD/AS undergoes a sudden increase in velocity equal to ∆V which is linked to the vorticity vector by the equation: ∆V= γ x nAS where nAS is a unit vector normal to the AD/AS and points in the direction for which discontinuities are applied. When applying the principle of vorticity flux conservation, it is found that the divergence of the γ field must be null, hence: ∇ ·γ = 0 (10) This equation implies that the distribution of discontinuities across an AD/AS is constrained and not completely free; in practice, blade-element analysis is used to evaluate the circulation around each airfoil section of the blades. This distribution is then redistributed to fix the spanwise component of the vorticity vector γ. All other components of γ are deduced by solving (10). Regarding the dynamics of the AD/AS interaction with the flow, a particle that crosses the AD/AS undergoes a step change in velocity which must be related to an attached system of forces responsible for changing the particle’s momentum. It can be demonstrated [7] that the expression for the system of forces attached to an AD or an AS is the Kutta-Jukowski relation: fROTOR = - ρ Vrel,av x γ (11) where Vrel,av is the velocity vector of flow particles measured relative to the AD or AS. This equation ensures that the flow total pressure is constant in the reference frame where the AS or AD is fixed. To model the WT action on the flow, other researchers propose the use of distributed volume forces within actuator volumes representing the swept area of the blades. The problem with this approach is that when actuator volumes become too thin, or when a rough numerical discretization of the actuator volume is used, spurious oscillations of flow properties are

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observed in the region close to the actuator volume (in great part due to high pressure variations, as discussed in Ref. [3]). The present formulation of AD/AS avoids such behavior. Furthermore, as presented in Ref. [3], it is consistent with other methods (AD-based methods like BEM models or differential AD analysis). 3 Conclusion Our research group’s decade of experience in using ADs to model WT rotors has proven that this concept can be successfully used to model wind parks [6]. The k-ε model has been shown to be accurate for modelling atmospheric flow turbulence, providing its constants are adjusted and a special treatment of the dissipation equation is applied in the vicinity of the AD surface. Recently, the concept of the AS has been studied and appears to be a promising tool for the study of wake aerodynamics. Comparative advantages of the AS model with respect to the AD model lie in the natural capacity of the AS model to account for the finite number of blades, contrary to AD-based models which require an ad-hoc treatment (like a tip factor model). Fig. 1 presents a comparison between simulation results using the AS concept and measurements for the MEXICO rotor recently tested in the DNW wind tunnel for the axial velocity component of the flow in the near-wake.

Figure 1: MEXICO Rotor: Comparison between AS simulations and measurements, Wind Tunnel

Velocity of 24 m/s. x=0 corresponds to the WT rotor axial position ; (a) r/R=0.55 (b) r/R=0.75 References [1] El Kasmi A. and Masson C. An extended k-ε model for turbulent flow through horizontal axis wind turbines. Journal of Wind Engineering and Industrial Aerodynamics, 96, 2008. [2] Alinot C. and Masson C. k-ε model for the atmospheric boundary layer under various thermal stratifications. Journal of Solar Energy Engineering, 127, 2005. [3] Leclerc C. and Masson C. Wind turbine performance predictions using a differential actuator-lifting disk model. Journal of Solar Energy Engineering, 127, 2005. [4] Masson C. and Smaïli A. Numerical study of turbulent flow around a wind turbine nacelle. Wind Energy, 9, 2006. [5] Masson C., Smaïli A., and Leclerc C. Aerodynamic analysis of hawts operating in unsteady conditions. Wind Energy, 4, 2001. [6] Ammara I., Leclerc C., and Masson C. A viscous three-dimensional differential/actuator-disk method for the aerodynamic analysis of wind farms. Journal of Solar Energy Engineering, 124, 2002. [7] Sibuet Watters C. and Masson C. Modelling of lifting devices aerodynamics using the actuator surface concept. Int. J. Num. Methods in Fluids, DOI: 10.1002/fld.2064, 2008.

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The dependence of wake losses on atmospheric stability characteristics

G.C. Larsen1, T.J. Larsen1, H.Aa. Madsen1, J. Mann1, A. Peña1, R. Barthelmie1 and L.

Jensen2

1Wind Energy Division Risø National Laboratory for Sustainable Energy

Technical University of Denmark - DTU P.O. Box 49, DK-4000 Roskilde, Denmark

2DONG Energy Power A/S Klippehagevej 22, DK-7000 Fredericia, Denmark

Corresponding author

G.C. Larsen [email protected]

Abstract Wakes cause significant power losses in wind farms. On average these losses amount to 10-20% of the wind farm power output. In addition to the power losses comes the increased (fatigue) loading of turbines operated under wake conditions, and wakes are therefore a major factor in wind farm economics. The average figures for power losses cover a multitude of effects primary related to the wind farm topology as well as the site wind field characteristics such as wind speed, wind direction, atmospheric turbulence and atmospheric stability [1], [2]. This paper offers a phenomenological explanation of the observed dependence of wind farm power production on atmospheric stability through modeling of the phenomenon and subsequent comparison with full-scale measurements. The modeling is based on the dynamic wake meandering (DWM) model [3], where downstream advected wake deficits are basically treated as passive tracers driven by the large-scale turbulent eddies in the atmospheric boundary layer (ABL). As the various ABL stability characteristics primarily affect the low frequency part of the turbulence spectra, and thus primarily the large-scale turbulent structures, the particular stability classification has a direct impact on the wake meandering, and thus in turn on the power production from downstream turbines. Compared to neutral atmospheric stratification, stable atmospheric stratification is characterized by a decrease in the energy content of the low frequency part of the turbulent spectra and thus in turn an attenuation of the downstream wake meandering. For a downstream turbine, sited in the mean wind direction from the wake generating turbine, this will lead to a more pronounced mean wake deficit, and thus to an increased mean production loss for this wind direction. As opposed to stable stratification, un-stable atmospheric stratification is characterized by an increase in the energy content of the low frequency part of the turbulent spectra leading to more violent wake meandering compared to the neutral situation. The downstream wake affected turbine will consequently experience an attenuated

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mean wake deficit, thus in turn leading to reduced mean production loss of this turbine for the considered wind direction. To facilitate inclusion of atmospheric stability classification in the wake meandering modeling, we fit the Mann spectral tensor model [4] to stable and unstable atmospheric stratification. The Mann model adapts well to the observations in all stability classes, although the model was developed for neutral conditions only. It slightly over-estimates the uw co-spectra at all heights [5], but fits well the u- and w-spectra as illustrated in the figure below.

Figure 1. Normalized spectra and co-spectra (NS) of the u (in blue) and w (in red) wind speed

components and uw-covariance (in black) from the sonics at 40 m for different stability conditions at Høvsøre, Denmark. The observations are shown in circles and the Mann

spectral model fit in solid lines. Results from the DWM simulations are compared to full-scale experimental results from two large offshore wind farms – the Horns Rev wind farm and the Nysted wind farm. Seven different stability classes are considered, and for each of these classes the power losses are analyzed in detail. An example of measured stability affected power production is shown in Figure 2, where the average power production for the 72 turbines at the Horns Rev wind farm is shown for a neutral stratification case and an unstable stratification case, respectively. Both cases relate to an ambient mean wind speed of 8 m/s, and a situation with the mean wind direction coinciding with direction of the turbine rows. The left hand figure shows the average power production for the unstable atmospheric stability scenario, whereas the right hand figure shows the average power production for the neutral atmospheric stability scenario. As seen, the power production is significantly lowered for the neutral case as compared with the unstable case.

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Figure2. Mean power production at the Horns Rev wind farm for unstable atmospheric stratification (left) and neutral atmospheric stratification (right).

Keywords: Atmospheric stability, dynamic wake meandering (DWM), full-scale power data, power loss, wake deficits, wake meandering. References [1] R.J. Barthelmie et al. (2007). Analysis of atmospheric impacts on the development of

wind turbine wakes at the Nysted wind farm. European Offshore Wind 2007, Berlin. [2] L. Jensen (2007). Analysis of array efficiency at Horns Rev and the effect of

atmospheric stability. 2007 European Wind Energy Conference and Exhibition, Milan, 7-10 May.

[3] G.C. Larsen et al. (2008). Wake meandering: A pragmatic approach. Wind Energy, 11, 377-395.

[4] J. Mann (1994). The Spatial Structure of Neutral Atmospheric Surface-Layer Turbulence. J. of Fluid Mech., 273, 141-168.

[5] A. Peña, S.-E. Gryning, J. Mann and C.B. Hasager (2009). Length scales of the neutral wind profile over homogeneous terrain, J. Appl. Meteor. Climatol.. In review.

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Do wind farms influence large scale turbulence?

G.C. Larsen1, J. Mann1, T.A. Ighil1 and A.S. Mouritzen2

1Wind Energy Division Risø National Laboratory for Sustainable Energy

Technical University of Denmark - DTU P.O. Box 49, DK-4000 Roskilde, Denmark

2DONG Energy Power A/S Klippehagevej 22, DK-7000 Fredericia, Denmark

Corresponding author

G.C. Larsen [email protected]

The dynamic wake meandering (DWM) model [1] is used for simple and fast modelling of the wind farm climates. The core of the model is a split of scales in the wake flow field, with large scales being responsible for stochastic wake meandering, and small scales being responsible for wake attenuation and expansion in the meandering frame of reference as caused by turbulent mixing. The model has 3 basic elements – a meandering model, a model of wake induced turbulence (i.e. mechanically generated turbulence originating from the wake shear field as well as from the break down of organized flow structures such as tip- and root vortices), and a model for the mean wake deficit as expressed in the meandering frame of reference. For solitary wakes, the model has been verified by comparing its performance with full scale LiDAR and pitot tube measurements of the wake flow field [2], [3], [4]. To consolidate the DWM model for wind farm applications, we need to consider a possible feed back from the presence of the wind farm on the large turbulence structures in the atmospheric boundary layer (ABL), which in the DWM model drives the wake meandering in lateral and vertical directions. For extremely large structures (e.g. manifested in wind direction changes) this feed back is clearly negligible. However, for less, but still large, scales the situation is less obvious. Assuming Taylor advection of turbulence and organized wake structures (i.e. wake deficits), the split of scales in the DWM context relates to a split frequency of the order of U/(2D), where D denoted the rotor diameter and U is the Taylor advection velocity. The aim of this analysis is thus to identify if the presence of a wind farm affects lateral turbulence components with frequencies below the split frequency, and moreover to investigate, in a qualitative manner, if this potential effect depends on the rotor sizes, the advection velocity and on atmospheric stability measures. The analysis is based on data from 3 full-scale Danish wind farms – the Nysted wind farm, the Vindeby wind farm and the Høvsøre test site. To simplify matters, all analyses are based on a simple configuration, where the wind direction is along a row of turbines. For the Høvsøre and Vindeby sites we thus investigate the effect on the large scale turbulence caused by 5 turbines in a row, whereas for the Nysted site we analyze the effect on the large scale turbulence caused by 8 turbines in a row. The turbine inter spacing is 300 m at the Høvsøre and Vindeby sites, whereas it is 867 m for the Nysted site.

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Basically, we compare the low-frequency part of the lateral turbulence spectra corresponding to respectively an undisturbed (i.e. reference) ambient recording (at turbine hub height) and a wake affected recording (at turbine hub height) downstream the last turbine in the considered row. Relatively long time segments are required for a satisfactory resolution of the low frequency part of the spectrum, which is in focus in the present analysis. Consequently record lengths of one hour was selected, reflecting the balance between on the one side the requested low frequency resolution and on the other side the statistical significance of the spectral estimates, which is essentially determined by the number of available segments. The statistical significance of the spectral estimates was enhanced by averaging the available number of spectra which, prior to the averaging, were normalized with respect to the variance of the respective reference recording to ensure a reasonable (i.e. uniform) weighting of the contributing spectra. Even though several years of data are available, the necessary directional binning (here appropriately defined as ideal direction ± 7°) reduces the usable part of the data set substantially, which in turn is reflected in somewhat scattered averaged spectra. The spectral scatter is further enhanced when additional binnings are introduced to resolve dependencies on advection velocity (or ambient mean wind speed) and atmospheric stability conditions. The former has an influence on the “transparency” of the wind turbines that potentially affect the downstream large scale turbulence. The latter has a direct influence especially on the low frequency part of the wind speed spectrum. The spectral scatter impede an exact definition of the frequency, finvariant, below which the large scale turbulence is unaffected by the presence of upstream wind turbines, especially if effects of both mean wind speed and atmospheric stability are attempted to be resolved. However, the data material gives good support for qualitative conclusions. Figure 1 indicates the dependence of finvariant on the mean wind speed.

Figure 1 Low frequency spectra from Høvsøre site in two velocity bins. The reference (blue) and wake affected (red) spectra coincide up to a higher frequency (finvariant ) for the higher wind

speed bin. Analysis of the data material led to the following conclusions:

1. An average value of finvariant over all mean wind speed and stability cases was estimated to approximately 0.004Hz from the Høvsøre and Nysted data (i.e. corresponding to an 80 m rotor);

2. finvariant seems to increase with the mean wind speed;

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3. finvariant tends to be larger for unstable atmospheric stratification; 4. finvariant does not seem to be notable affected by turbine inter spacing nor the number

of upstream turbines, or rather that if affected, these potential influences counter balance each other in the Nysted (8 turbines; 10.5 rotor diameter spacing) and Høvsøre (5 turbines; 3.75 rotor diameter spacing) cases; and

5. Comparisons of Vindeby and Høvsøre data result in a clear indication of increasing finvariant with decreasing rotor diameter.

Comparing Høvsøre and Vindeby results, Figure 2 illustrates the dependence of finvariant on the rotor size for the mean wind speed bin extending from 6 m/s to 7 m/s. The rotors at the Høvsøre site have a diameter of 80 m, whereas the rotors at the Vindeby site have a diameter of 35 m.

Figure 2 Low frequency spectra from Høvsøre site (left) and Vindeby site (right) for the velocity bin extending from 6 m/s to 7 m/s. The reference spectra (blue) and the wake affected spectra (red) coincide up to a higher frequency (finvariant ) in the Vindeby case.

Keywords: Atmospheric stability, dynamic wake meandering, feedback, large eddies, turbulence, wind turbines. References [1] G.C. Larsen et al. (2008). Wake meandering: A pragmatic approach. Wind Energy 11,

377-395. [2] Bingöl, F.; Mann, J. and Larsen, G.C. (2009). Lidar Measurements of Wake Dynamics,

Part 1: One Dimensional Scanning. Accepted for publication in Wind Energy. [3] Trujillo, J.J.; Bingöl, F.; Larsen, G.C.; Mann, J. and Kuehn, M. (2009). Lidar

Measurements of Wake Dynamics, Part 2: Two Dimensional Scanning. Accepted for publication in Wind Energy.

[4] H.Aa. Madsen, G.C. Larsen, T.J. Larsen and N. Troldborg (2009). Calibration and validation of the Dynamic Wake Meandering model implemented in the aeroelastic code HAWC2. Submitted for publication in Journal of Solar Energy Engineering.

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RANS simulations of a wind-farm with the application of the actuator disc concept

Giorgio Crasto, Francesco Castellani, Arne Reidar Gravdahl.

Corresponding author Giorgio Crasto, Ph.D.

Software Developer, WindSim AS, c/o Studio Rinnovabili, Via Lagrange, 1 - 00197 Roma

Tel +39 06 8073469 Fax+39 06 80693106 www.windsim.com

Abstract The wakes of wind turbines in a wind farm are modeled with the actuator disc concept: the computational cells designing the rotor exert resistive forces calculated directly from the thrust curve. The atmospheric boundary layer is modeled with RANS simulations on a structured mesh done with hexahedral cells. The wakes interact with each other and with the topography giving a more realistic description of the flow within the wind park. The porpoise of this methodology is to adopt it in the calculation of the annual energy production of a wind park in order to achieve a more precise energy output computation.

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Mesoscale and turbulence effects on wind farms

Julian Hunt

CERC, University College London, Trinity College Cambridge Abstract The paper reviews how wind energy varies greatly on regional scales which need mesoscale models to evaluate, and some broad physical understanding is also needed in order to understand the progressively increasing effects of climate change. Wind farms significantly perturb the airflow within them on a range of scales varying from that of the wakes of blade to wakes of turbines to the scale of the farm itself, and finally to scales that extend over 100km downwind (as data of decreased rainfall indicates in southern USA). Recent research on the sharp boundaries of wakes shows why the impact of wakes on downwind turbines can be very short time scale. The porous effect and mesoscale perturbations are important for the efficiency of the wind farm and for its wider environmental effect. New modelling is being developed on all these scales. (Hunt, Orr, Rottman, Capon, Q. J. Royal Met. Soc. 2004; Owinoh et al., BLM 2005; Westerweel et al., Phys Rev Lett 2005; Hunt, Eames, Westerweel, J. Fluid Mech. 2006).

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Numerical simulations of the turbulent logarithmic layer

Javier Jiménez

School of Aeronautics, Universidad Politécnica, 28040 Madrid, SPAIN and Centre for Turbulence Research, Stanford University, Stanford CA, USA

Abstract Direct numerical simulations over the past two decades have provided a lot of new information on the dynamics of wall-bounded turbulent flows. Up to recently, they were limited to relatively low Reynolds numbers, which made them useful mostly for investigating the near-wall viscous layer over smooth plates, but in the last few years they have moved into Reynolds numbers that, although still very far from atmospheric values, begin to overlap experiments, and to include a nontrivial range of relevant length scales. The simulations presently available are in the order of friction Reynolds numbers of Reτ= 1000−2000, for flows ranging from turbulent pipes to channels, smooth and rough flat-plate boundary layers, and the Ekman layer. Those numbers will likely double in the next 3-5 years. Anything above Reτ= 700 − 1000 has an incipient logarithmic layer, and can be used to investigate multiscale physics. Some of the most interesting results from these simulations are those regarding the interaction of structures of different sizes and at different wall distances. For example, it had been assumed for a long time that boundary layers grew from the ground up, which had led to the conjecture that the detailed structure of the rough logarithmic layer would be very different from the smooth one. This has proved not to be the case, at least for normal k-type roughness. The only effect above a layer of the order of a few roughness heights is to displace the mean velocity profile by a constant amount, but both the fluctuations and the structures remain largely unaffected. On the other hand there seems to be a clear effect of the larger outer scales on the near-wall ones. For example, the intensities in boundary layers are stronger that in internal flows, although they seem to be of very similar sizes. The higher intensities can be traced to the inactive motions induced near the wall by pressure fluctuations from very large outer structures, and the difference between internal and external flows can be traced to the irrotational intermittency near the edge of the latter. In the atmosphere, those structures can have periods of the order of minutes, and lengths of several hundred meters. Their effect on the near-wall structures is basically a modulation. The smaller structures, whose characteristic frequencies are higher, essentially live in a time-dependent local boundary layer generated by the larger ones. Most of this information has been obtained from simulations and experiments of canonical wind-tunnel flows, but much of it has been validated with atmospheric observations, for example in the Utah salt flats. Recently, simulations and theoretical models of the Ekman layer and of stably stratified channels have began to appear. They are important because both stratification and rotation modify preferentially the largest scales, and therefore the interaction effects just mentioned.

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Wind tunnel simulation of the wakes of large wind turbines in off-shore stably stratified flow

F. Pascheke, P. E. Hancock

EnFlo Laboratory

Faculty of Engineering and Physical Sciences, University of Surrey Guildford, Surrey, GU2 7XH, UK

Tel: +44 1483 689625

Corresponding author P. E. Hancock

[email protected] Abstract Measurements have very recently been made of a wind turbine wake in both neutral and stably stratified flow in the EnFlo wind tunnel at the University of Surrey. The wind tunnel is capable of creating neutral, stable and unstable atmospheric boundary layers in its 20m long working section, by means of a controllable-temperature inlet heaters and side panels. The measurements were made in the wake of a rotating model wind turbine 1/300-scale (of 5MW size) as part of a UK-EPSRC-funded SUPERGEN consortium project. Velocity measurements were made using two-component laser Doppler anemometry between 0.5 and 10 diameters downstream. This probe was combined with a ‘cold-wire’ temperature probe in order to measure the local turbulent heat flux and other quantities in the stratified cases. In the work so far the Monin-Obukov length was about 290m at full scale – about two rotor diameters – which is in the moderately stable band of 200m-1000m (Barthelmie, 1999). Simulation of off-shore wakes is particularly constrained because i) at wind tunnel scale the inherently low surface roughness can be below that for fully rough conditions, ii) the power required to stratify the flow varies as the square of the flow speed, and could easily be impractically large, iii) low flow speed leads to low blade Reynolds number and unrepresentative blade lift characteristics. The boundary layer simulation and the model wind turbines have therefore been designed against these constraints. The measurements show that even in mild stratification the vertical development of the wake deficit can be completely inhibited. Qualitatively, one would expect at least some reduction arising from the stabilizing influence on vertical fluctuations. The width in contrast develops at about the same rate. As anticipated, the wake development is slower in the stable case because of the lower level ambient turbulence. The maximum deficit is at a lower height than it is for neutral flow. Various aspects of the turbulence in the wake have also been measured. Further work will include wakes from multiple machines, as has been studied in neutral conditions. Keywords: wind turbine wakes, stable stratification, wind tunnel simulation. References Barthelmie, R. J., (1999). “The effects of atmospheric stability on coastal wind climates. Meteorol. Appl. 6, 39-47.

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Large Eddy Simulation study of fully developed wind-turbine array boundary layers

Marc Calaf +*, Charles Meneveau ++, Johan Meyers +++

* Visiting student at the Department of Mechanical Engineering, Johns Hopkins University, 3400 North Charles Street, Baltimore MD 21218, USA

+ Laboratory of Environmental Fluid Mechanics and Hydrology, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland. [email protected]

++ Department of Mechanical Engineering, Johns Hopkins University, 3400 North Charles Street, Baltimore MD 21218, USA, [email protected]

+++ Department of Mechanical Engineering, Katholieke Universiteit Leuven, Celestijnenlaan 300A bus 2421, B3001 Leuven, Belgium. [email protected]

Corresponding author

Marc Calaf [email protected]

Abstract It is well-known that when wind turbines are deployed in large arrays, their efficiency decreases due to complex interactions among themselves and with the atmospheric boundary layer (ABL). For wind farms whose length exceeds the height of the ABL by over an order of magnitude, a “fully developed” flow regime can be established. In this asymptotic regime, changes in the stream-wise direction can be neglected and the relevant exchanges occur in the vertical direction. Such a fully developed wind-turbine array boundary layer (WTABL) has not been studied systematically before. A suite of Large Eddy Simulations, in which wind turbines are modeled using the classical “drag disk” concept, are performed for various wind turbine arrangements, turbine loading factors, and surface roughness values. The Smagorinsky subgrid scale model with wall damping, as well as the Lagrangian, scale-dependent dynamic model, have been implemented and results compared. Mean velocity distributions show little difference, with slightly larger wake deficits for the non-dynamic Smagorinsky model. Results are used to develop improved models for effective roughness length scales experienced by the ABL. The effective roughness scale is often used to model wind turbine arrays in simulations of atmospheric dynamics at larger (regional and global) scales. Results from the LES are compared with several existing models for effective roughness lengths. Based on the observed trends, a modified model is proposed that includes effects of a finite rotor disk region in the profile, showing improvement in predicted effective roughness lengths. Keywords: WTABL, effective roughness length, LES, subgrid scale model.

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Comparison and Validation of BEM and Free Wake Unsteady Panel Model with the MEXICO Rotor Experiment

D. Micallef1, M. Kloosterman2, C. Ferreira3, T. Sant4, G. van Bussel5

1DUWIND, TUDelft, Faculty of Aerospace Engineering, The Netherlands and University of

Malta, Department of Mechanical Engineering, Malta. 2,3DUWIND, TUDelft, Faculty of Aerospace Engineering, The Netherlands.

4University of Malta, Department of Mechanical Engineering, Malta. 5Professor, DUWIND, TUDelft, Faculty of Aerospace Engineering, Kluyverweg 1, 2629 HS,

Delft, The Netherlands

Corresponding author D. Micallef

[email protected] Abstract The Model Rotor Experiments under Controlled Conditions (Mexico) project aimed at creating database of wind turbine rotor aerodynamic measurements under controlled conditions, for validating and improving wind turbine rotor aerodynamic simulation methods. An extensive measurement program was carried out on a three bladed 4.5m diameter rotor model in the DNW wind tunnel (test cross section of 9.5 × 9.5m). The measurements consisted of pressure distribution along the chord at five spanwise locations and Stereo Particle Image Velocimetry at certain location of the flow field, including tip vortex. The measurements included both yawed and axial conditions. In this work we present some of the results of the MEXICO experiment and use them for validation and comparison between blade element momentum codes and free wake unsteady potential flow codes. The comparison is performed with results for the non-yawed and yawed case, with special focus on the evaluation of the effect of yaw. Load and power curves as well as spanwise load distributions in axial flow (such as fig. 1 and fig. 2) are presented comparing the results from experiment with a BEM model without 3D effect corrections. This helps in identifying the how much the use of 2D airfoil data affects the computations. These results are also shown for the case of yawed flow. 3D airfoil data was derived from experiment using the angles of attack found from the BEM model. This was also done for the yawed flow cases where hysteresis loops were observed highlighting the dynamic nature of the flow. A direct free wake code was also used for axial flow cases and tip vortex trajectories were compared with the PIV data (see fig. 3). The tip vortex strength decay in the near wake was also compared (see fig. 4) along with a comparison between the flow field close to the tip vortex and the rolled up vortex sheet from the free wake model. Keywords: MEXICO experiment, BEM, Free Wake Code.

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References Model Experiments in Controlled Conditions(MEXICO) - Final Report M.H.M. Kloosterman, \emphDevelopment of the Near Wake behind a Horizontal Axis Wind Turbine Including the development of a Free Wake Lifting Line Code - M.Sc Dissertation, TUDelft.

Figure 1 -Example validation of BEM simulations with experimental data, thrust coefficient vs. tip speed ratio, non-yawed flow case.

Figure 2 - Example validation of BEM simulations with experimental data, power coefficient vs. tip speed ratio, non-yawed flow case.

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Figure 3 - Simulation with free wake model (blue) vs. experimental surface of the tip vortex (green).

Figure 4 - Experimental vorticity data of tip vortex evolution.

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Experimental and numerical investigation of the 3D VAWT wake.

Carlos Ferreira ∗, Claudia Hofemann †, Gijs van Kuik ‡, Gerard van Bussel §

∗DUWIND, TUDelft, The Netherlands. †DUWIND, TUDelft, The Netherlands.

‡Professor, DUWIND, TUDelft, The Netherlands. §Professor, DUWIND, TUDelft, Kluyverweg 1, 2629 HS, Delft, The Netherlands

Abstract The Vertical Axis Wind Turbine, in its 2D form, is characterized by a complex unsteady aerodynamic flow, including dynamic stall and blade vortex interaction. Adding to this complexity, 3D flow brings spanwise effects and the presence of trailing vorticity and tip vortices. The objective of the current paper is to bring insight into the 3D development of the near wake of a H-VAWT, understanding: • Spanwise blade load distribution, upwind and downwind blade passages. • Trajectory of tip vortices, including inboard movement and radial expansion of shed and trailing vorticity. • 3D effects on the efficiency of the VAWT. • Blade vortex interaction of upwind tip vortex with downwind blade passage. • Induction due to trailing vorticity. The investigation is composed of experimental wind tunnel research with Stereo-PIV and modeling of the rotor and wake with a 3D unsteady panel method. A two bladed H-Darrieus VAWT model was tested in the low speed/low turbulence wind tunnel at Delft University of Technology. Stereo-PIV measurements were used to visualize the flow in the near wake focusing on the flow field around four tip geometries. The measurement planes cover several sections of the rotor volume, allowing for a reconstruction of the evolution of the tip vortex. The formation, convection and dissipation for each tip vortex were located and quantified (see example Figure 1). The experimental PIV data is used to validate the 3D, unsteady, multibody, free-wake panel method developed to model a VAWT (see example Figure 2). The combination of the results of the panel model validated by experiments, in particular the Stereo PIV results, allows to understand the impact of the near wake development in the upwind blade passage, as well as the energy conversion process at the downwind blade passage.

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Figure 1: Experimental PIV measurement of vorticity in planes y R = −0.42, −0.21, 0 ,0.21

and 0.42, for azimuth angle of the rotor θ = 110, 120 and 130.

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Figure 2: Comparison of 3D reconstruction of experimental PIV iso-vorticity surface ( Ωc

U∞ = 5) and near wake from panel model, at θ = 150.

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Development of a process chain for a detailed wake simulation of horizontal axis wind turbines

K. Meister, Th. Lutz, E. Krämer

Institute of Aerodynamics and Gas Dynamics, Universität Stuttgart Pfaffenwaldring 21, 70569 Stuttgart, Germany Tel:+4971168560258, Fax: +4971168553402

Corresponding author

K. Meister [email protected]

Abstract There is an increasing interest to refine the numerical simulation of the unsteady aerodynamics, the wake development and its interaction with atmospheric boundary layer and gust to finally predict the transient loads and extreme loads acting on the blades of turbines in the first row and the ones behind. For this purpose a CFD based process chain is being developed and applied at the institute of aerodynamics and gasdynamics (IAG), University of Stuttgart. The process chain consists of a grid generator with scripting capability for automated meshing, the block structured flow solver FLOWER, which is provided by the German Aerospace Center (DLR) and optional of a multibody simulation code with a grid morpher for aeroelastic simulations. The aeroelastic coupling scheme is described in [1] along with application examples. A library of scripts has been developed that enables a fast generation of high-quality structured RANS meshes by means of the commercial mesh generator Gridgen. The scripts include a parametric representation of the blade geometry and the possibility to control the discretisation and Reynolds-dependent mesh refinement. With this approach it is possible to create case optimized blade grids on a desktop computer within a few minutes. The meshing of the blades bases on airfoil sections of the blade geometry. Therefore the number of cuts and their location on the geometry are defined manually. The airfoil sections are then directly extracted from an IGES-file which contains the blade geometry and imported to the meshing process. The blade boundary layer is fully resolved by about 30 cells in wall normal direction with an anticipated nominated wall distance of the first cell of about y+ = 1 even in span width. To enable better quality the mesh is twisted to fit to the local incidence of each airfoil section. Moreover the mesh in the near wake of the blades is refined to reduce the numerical dissipation and to enable a detailed simulation of the wake development. An example of a meshed blade and its IGES geometry is shown in Fig. 1. Besides the blades tower and nacelle are simulated, too. The meshes are still handmade, but block structured, too. As a grid connection between the different grids is very complicated, overlapping Chimera meshes are used for a complete simulation to ensure high mesh quality (Fig. 2).

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Fig. 2: View of a meshed blade (green) surrounded by an circular disc grid (red) with an background grid (blue) [2]

With the described process chain it is possible to perform URANS simulations of wind turbines with detailed analysis of the boundary layer and the near wake. The process chain reduces preparation time for the meshing and the structured meshes make effective calculations on vector computers possible. Near the grid generation the process chain contains the flow solver FLOWER for the URANS simulations. This code solves the three dimensional RANS equations in integral form on block structured grids. FLOWER is formulated in finite-volume method, and uses the cell vertex or the cell centered approach. FLOWER includes more than 10 models for turbulence modelling like the zero equation Baldwin-Lomax model, the two equation Wilcox k-ω model and the Reynolds Stress models from Wilcox [3]. An example for FLOWER URANS simulations of a wind turbine, with tower and nacelle, a number of 11 million cells with a rotation angle of 1° per time step at a wind speed of 15 m/s

Fig. 1: Blade geometry in IGES format and meshed blade; not all cells are shown [1]

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[4]. The results of these transient simulations were aerodynamic coefficient and load distributions for an azimuth angle between 0° and 360°. The pressure coefficient distribution for the simulated wind turbine at a certain time step is shown in Fig. 3.

Currently the process chain is being applied for the simulation of the MEXICO wind turbine [5] which has been measured in the German-Dutch Wind Tunnel (DNW), where detailed PIV wake measurements have been extracted. The simulation of the MEXICO wind turbine is part of the MexNext project where the simulation results will be compared to the MEXICO measurements. After simulation of the wind turbine under free stream conditions the turbine will be simulated under consideration of wind tunnel environment, and compared to the MEXICO results. Keywords: wind turbine, mesh generation, CFD References: [1] M. Kamruzzaman, K. Meister, Th. Lutz, M. Kühn, E. Krämer, “Wind Turbine Aerodynamics and Aeroacoustics at University of Stuttgart - An Overview of Research and Development“, ICDRET (2009) [2] S. Streiner, S. Hauptmann, M. Kühn, E. Krämer, “Coupled Fluid-Structure Simulations of a Wind Turbine Rotor“, DEWEK (2008) [3] N. Kroll, J. K. Fassbender, “MEGAFLOW - Numerical Flow Simulation for Aircraft Design”, Springer Verlag Berlin/Heidelberg/NewYork, ISBN 3-540-24383-6 [4] M. Hohlfeld, “CFD URANS-Berechnungen einer Windkraftanlage unter Berücksichtigung von Turm- und Gondelstruktur“, Diploma Thesis, IAG, (2009) [5] H. Snel, G. Schepers, A. v. Garrel, S. Barth, “The MEXICO project: Analysis of yaw measurements and comparison with existing models“, EWEC, (2008) [6] G. Schepers, “Progress of IEA Task 29 ‘MexNext’“,IEA Wind ExCo meeting #63, (2009)

Fig. 3: Pressure coefficient distribution on a wind turbine [4]

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LiDAR measurements of full scale wind turbine wake characteristics

Kurt S. Hansen1, Gunner Chr. Larsen2, Karen Enevoldsen2, Jakob Mann2

1 Department of Mechanical Engineering, Fluid Mechanics, Nils Koppels Allé, DTU-

Building 403, Technical University of Denmark, DK-2800 Lyngby; Email: [email protected] 2 Wind Energy Department, Risø National Laboratory for Sustainable Energy, Technical

University of Denmark, P.O. 49, DK-4000 Roskilde, Denmark Abstract Full scale wind speed measurements, recorded inside the wake of an operating 2MW/80m wind turbine,has been performed during the spring 2009, as part of the EU-TOPFARM project. Longitudinal wind speeds in wake cross sections are measured with a LiDAR system mounted in the rear of the nacelle. The experimental setup, the amount of data, preliminary analysis and limitations of using LIDAR measurements to identify the wake dynamics will be presented. Resolving the wake in the meandering frame of reference further allows for identification of the wake characteristics both in terms of wake deficit and wake turbulence. Summary As part of the EU-TOPFARM project a full-scale wake measurement experiment was successfully performed in the beginning of 2009 with the primary aim of characterizing the deficit as well as the turbulence in wakes caused by a 2MW wind turbine [1]. The wake dynamics was resolved using a LiDAR based wind speed scanning system. Recent analysis of the huge amount of data, recorded during this measuring campaign, demonstrates a close correlation between the down stream wake meandering and the large scale part of the turbulent inflow field. This has also been shown for a smaller turbine [2]. Resolving the wake in the meandering frame of reference further allows for identification of the wake characteristics both in terms of wake deficit and wake turbulence. The primary focus in the present experiment is on characterization of wake turbulence. The turbine in question is located inside a small wind farm consisting of 8 x 2 MW wind turbines. The LiDAR system has been mounted in the rear of the nacelle and has a variable focus distance, which enables wake flow fields to be measured in arbitrary “cross sections” ranged from 0.5 – 2.5 rotor diameters downstream from the wake generating rotor. The LiDAR system has a (vertical) tilt range of ± 8º and a (horizontal) pan range of ± 25º. The wake deficits are thus measured over an approximately rectangular cross section where the depth of the wake deficit obviously depends on the actual focus distance. The number of velocities measured in each cross section is in the current configuration approximately 400, the recording of which takes approximately 1.15 second. The cross section sampling rate is thus roughly 0.9 Hz, which is considered sufficient for the intended application (i.e. sufficient for considering a cross section scan as “instantaneous” in a wake meandering context). The wake measurements have been synchronized with turbine production data and with recordings from a nearby 90 m reference meteorological mast equipped with wind speed and wind direction sensors in various levels covering the rotor disc.

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Results from initial analysis of 3 seconds wake deficits on Figure 1 show how the wake centre moves during 600 seconds - both in transversal and vertical direction. Furthermore the aligned averaged measurements along radial annuli in terms of mean speed deficit and turbulence are shown also shown on Figure 1. These measurements have been recorded at a power production of 275 kW (Vhß6 m/s). The paper will include analyses of the degree of rotationally symmetry of the wake deficit, of wake expansion and of wake turbulence in the wake near field. The in-homogeneity of the near wake turbulence field will be quantified in terms of turbulence standard deviation and – if possible – in terms of wake turbulence spectral characteristics.

Figure 1: Mean characteristics of the aligned wind turbine wake 2 rotor diameters

downstream at Vh~6 m/s. References [1] “LiDAR measurements of full scale wind turbine wake characteristics” by Kurt S. Hansen, Gunner Chr. Larsen, Karen Enevoldsen & Jakob Mann; presented at EWEC2009 in Marseille. [2] “Lidar measurements of wake dynamics – Part I: One dimensional scanning” F. Bingöl, J. Mann and G. C. Larsen. Under review in Wind Energy, 2009

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Decaying Coherent Eddy Structures and Turbulent Fluctuations in Wind Turbine and Wind Farm Wakes - analysis of airborne

measurements

Abha Sood (1) and Jens Bange (2)

(1) ForWind, Centre for Wind Energy Research, Carl von Ossietzky University Oldenburg, Germany.

(2) Institute of Aerospace Systems, Technical University Braunschweig, Braunschweig, Germany.

Abstract Turbulent wakes produced by wind turbines modify the ambient inflow wind conditions considerably for the wind turbines within large offshore wind farms. Considering the immense scale of the investments planned in the coming years for the exploitation of offshore wind energy, with a very large number of relatively closely spaced wind parks, the wake interaction within and downstream of offshore wind parks must be well represented in wind farm models under real atmospheric conditions. For optimizing parameterization within the - state of art - models and developing new models, very precise high resolution turbulence measurements are required. These turbulence measurements have to cover the air flow up- and downstream of wind parks, and ideally also between individual turbines. Since ground stations and measurement towers offer only isolated point measurements, and remote sensing methods rely strongly on assumptions on the turbulent structure of the lower part of the atmospheric boundary layer, the best strategy to obtain precise in-situ data are airborne measurements. Probably the most accurate airborne measurement platform offering highest spatial and temporal resolution of thermodynamic quantities is the helicopter-borne turbulence probe Helipod. The Helipod is attached to a 15 m rope and carried below a helicopter and outside the downwash area of the rotor blades at 40 m/s. At a sampling rate of 500 Hz, measurements of the wind vector, temperature and humidity resolve sub-meter turbulence but also large (e.g. convective) structures. Vertical profiles and horizontal legs can be flown between 1500 m and a few meters above the surface, although the latter is limited by local flight safety rules (settlements, power lines etc.). To demonstrate the feasibility of using the Helipod probe to depict interaction of the ambient flow with turbulent wake structures from the large wind turbines and its decay downstream, a series of high spatial and temporal resolution wind temperature and humidity measurements were conducted on multi-megawatt wind turbines wakes during the measurement campaign "OffCoast" in the German Bight on the 9. May 2008. Two wind turbines of ENERCON E-126, with a rotor diameter of 126 m (413 ft) and hub height of 135 m (450 ft) with 6 MW rated power, were installed since October 2007 at the onshore coastal testing site in Rysumer Nacken near Emden in the northwest of Germany. The two BARD 5.0 turbines designed for offshore wind farms with a rotor diameter of 122 m (410 ft) and hub height of 90 m also started wind energy production at this site on the 3. May, 2008. In preliminary investigations of the high frequency turbulence measurements of inflow conditions in front of the wind turbines and wake conditions at two measurement planes in between and in the far wake at

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three heights, the turbulence intensity and the structure functions were determined and the spatial statistics of the measured inflow and wake was estimated for three turbulence components (along-wind, across-wind, and vertical). The decay of measured turbulence characteristics in the existing atmospheric stability conditions are discussed and compared with the current empirical modelling approaches based primarily on wind tunnel measurements.

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Temporal and spatial study of the meandering phenomenon

G. España, S. Aubrun, S. Loyer, P. Devinant

PRISME Institute, 8 rue Leonard de Vinci F-45072 Orléans Cedex 2, France Abstract At the present time, a large part of numerical and experimental approaches usually model the wind turbine wake as a steady phenomenon. But, field observations showed an unsteady behaviour of the wake (Ainslie, 1988, Bingöl, 2009). Consequently, steady models certainly underestimate the fatigue that a wind turbine in the wake of another one faces. This observed unsteady phenomenon is the so-called wake meandering where the whole wake is seen to oscillate randomly. The reasons for this random flapping are not yet well known. Two possible sources have been underlined: on one hand, Medici and Alfredsson (2005), using a wind turbine model in a wind tunnel, explained the observed wake flapping as a consequence of the vortex shedding (as for bluff bodies). On the other hand, Larsen et al. (2008) developed an analytical model based on the role of the large scale vortices contained in the atmospheric boundary layer (ABL). The goal of the present work was to prove the role of the large turbulent length scales of the ABL and to study the development of the wake. For that, the ABL and a wind turbine were modelled in a wind tunnel at a geometric scale of 1:400. Mean and turbulent properties of a moderately rough ABL were reproduced. The wind turbine was modelled with a 100mm diameter porous disk, according to the actuator disk concept. To dissociate the random flapping (meandering) of a wind turbine wake and the periodic oscillations downstream of a bluff-body (vortex shedding), investigations has been carried out on both the porous and a solid disk (same diameters). Two measurement approaches were used. Firstly, hot wire anemometry, to investigate the meandering phenomenon from a temporal point of view. For that, velocity spectra and space-time correlations had been registered by two probes in different precise regions of the wake. This temporal study allowed to distinguish the wake beahaviours donwstream of the porous and the solid disk. Secondly, 2D Particle Image Velocimetry was used to focus on the spatial development of the oscillating wake, up to 6 rotor diamaters downstream. Special post-processing had been developed to evaluate the standard deviation and the width of the wake. This study enabled the spatial characterisation of the meandering wake, and comparisons with numerical schemes (Trujillo, 2009). To emphasize the role of the large turbulent length scales of the atmosphere, all the measurements and post-processing were performed not only in ABL conditions but also in homogeneous and isotropic turbulent conditions. The main difference between these two types of flows was the longitudinal integral length scale in the streamwise direction Lux. In the modelled ABL, Lux was about ten times larger than the disk diameter whereas Lux was about ten times smaller in isotropic conditions. References • Ainslie, J.F, 1988. Calculating the flow field in the wake of wind turbines. Journal of Wind Engineering and Industrial Aerodynamics 27, 213-224.

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• Bingöl, F., Mann, J., Larsen, G.C., 2009. Lidar measurements of wake dynamics Part 1 : One dimensional scanning. Wind Energy. Submitted. • Larsen, G.C., Madsen, H.A., Thomsen, K., Larsen, T.J, 2008. Wake meandering: a pragmatic approach. Wind Energy 11, 377-395. Doi:10.1002/we.267. • Medici, D., Alfredsson, P.H., 2006. Measurements on a wind turbine wake. 3D effects and bluff body vortex shedding. Wind Energy 9, 219-236. Doi:10.1002/we.156. • Trujillo, J.J., Kühn, M., 2009. Adaptation of a Lagrangian dispersion model for wind turbine wake meandering simulation. Proceedings of the European Wind Energy Conference, March 16-19, 2009. Marseille, France.

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Influence of topography and wakes on wind turbulence. Measurements and interpretation of results

A. Jiménez1, E. Migoya1, M. Esteban2, J. García1, D. Giménez2, A. Crespo1.

1Laboratorio de Mecánica de Fluidos

Escuela Técnica Superior de Ingenieros Industriales, Universidad Politécnica de Madrid C/ José Gutiérrez Abascal, 2, Madrid 28026, Spain

Tel:+34913363152, Fax: +34913363006 2 Gamesa Eólica S.A.U., Polígono Agustinos, 31013, Pamplona, Navarra.

Corresponding author

A. Jiménez [email protected]

Abstract Wind data from three different locations have been analyzed. All of them have complex topography, and in two of them there are wind farms installed. For specific wind directions the measuring masts are either affected by the topographic obstacles, or under the influence of the wakes of the wind turbines, and in some case both effects are relevant. Time series of the three velocity components are measured using sonic anemometers at several heights. From ten minute series, average velocity, standard deviations and spectra are obtained. Length scales are inferred from the spectra. Besides, by combination of measurements at two heights spectral coherence is also calculated. All these magnitudes are compared with their corresponding values calculated according to different standards for flat uniform terrain. Also, calculations have been carried out using UPMPARK code for wakes, and WAsP engineering for terrain effects, however, the results obtained are not always in agreement with measurements. Some complementary ad hoc rules, based on the physical interpretation of the flow processes, are suggested to make quantitative estimations of the flow characteristics that improve the agreement with the measurements.

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Advances in wind tunnel testing of wind farm

Sebastián Franchini1, Álvaro Cuerva Tejero, Oscar López García

UPM, 1 [email protected] Abstract The aim of this work is to study the aerodynamic behaviour of porous disks in order to establish a procedure to simulate wind turbines operating in a wind farm. When operating, a wind turbine, creates a deficit in the average momentum downstream in its wake, induces rotational components and increases the intensity of turbulence of the wake. A porous disk immersed in a flow stream produces a force in the direction of flow and creates a wake in which there is a deficit in the average momentum and increased intensity of turbulence. Based on these similarities, a characterisation of the aerodynamic behaviour of porous disks is presented, towards to establish correlations between the behaviour of porous disks and wind turbines, with the goal of simulating a wind turbine at various operating conditions in a wind tunnel, as well as several wind turbines arranged in a wind farm. Moreover, the idea of modelling wind turbines with a porous disk is also based on the concept of actuator disk applied by the Momentum Theory. In this theory a circular cross-section immersed in a flow of a fluid extracts kinetic energy from the flow and produces a wake characterized by a lack of momentum. Ten disks with different porosities were studied through wind tunnel tests. The experiments consisted of determining the drag coefficient from the measured force and simultaneously measure the wind speed in the wake of each model. The early analysis of the results shows promising evidence that it will be possible to simulate the behaviour of wind turbines using porous disks.

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Wake measurements of a multi-MW wind turbine with long range lidar

Y. Käsler1, S. Rahm1, R. Simmet1, J.-J. Trujillo2

1Deutsches Zentrum für Luft- und Raumfahrt e. V. (DLR)

Institut für Physik der Atmosphäre, Abteilung Lidar Münchner Str. 20, 82234 Oberpfaffenhofen, Germany

Tel:+498153283519, Fax: +498153281271

2Stiftungslehrstuhl für Windenergie (SWE) Universität Stuttgart

Allmandring 5 B, 70550 Stuttgart, Germany

Corresponding author Y. Käsler

[email protected] Introduction Long range Doppler lidar (LIDAR-Light Detection and Ranging) measurements were carried out at a site near the coast-line in Bremerhaven. A 5 MW wind turbine of the type Multibrid M5000, which is the prototype for the first German offshore wind farm “alpha ventus”, is located there. The aim of the measurement campaign was to get information about the ambient wind field of this turbine. The characterization of the wake of the wind turbine was a matter of particular interest. Here we present the measurement setup and preliminary results. Measurement technique and experimental setup Lidar is a remote sensing technique where a laser beam is transmitted into the atmosphere and the backscattered light is detected. This provides information about the line-of-sight (LOS) component (component in beam direction) of the wind vector. For the measurements presented in this abstract a 2 µm pulsed Doppler lidar based on the transceiver unit of a MAG-1 instrument of CLR Photonics was used [1]. This laser system has been modified by the DLR and successfully used for wind and turbulence measurements from the ground, as well as from the research aircraft, in the past [2]. Different scan patterns at variable scan speeds are possible. The measurement range is between 500 m and more than 10 km. The main parameters of the 2 µm pulsed Doppler lidar are summarized in Table 1.

Slave laser (Tm:LuAG) Wavelength 2.022 µm

Repetition rate 500 Hz Pulse energy 1.5 mJ Pulse length 0.5 µs

Telescope off-axis type

aperture: 10 cm

Scanner double wedge with variable speed

Measurement range 500 m - >10 km

Table 1: Main parameters of the 2 µm pulsed Doppler lidar.

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The 2 µm lidar was mounted in a container and placed on a field in a distance of about 1850 m away from the Multibrid M5000 wind turbine. Two scanning techniques to analyse the wake of this multi-MW turbine were carried out: elevation scans (Figure 1(a)) and azimuth scans (Figure 1(b)). For the elevation scans the azimuth angle of the laser beam was kept constant whereas the elevation angle was varied. For the azimuth scans the elevation angle was always the same but the azimuth angle was changed. This results in a scan almost parallel to the ground at a distance of 1850 m because elevation angles did not exceed 5 °. The scan patterns are illustrated in Figure 1. In this figure it can also be seen that there are a lot of other wind turbines in the measurement terrain. Effects of these turbines can be observed in our measurements as well.

Results Figure 2 shows the line of sight wind speed depending on width and range of an azimuth scan with a constant elevation of 3.3 °. The azimuth angle was between -8 ° and 22 ° which corresponds to an expansion in width of about 1300 m at a distance of 2.5 km from the lidar. The 2 µm lidar is located at a range of 0 and the Multibrid M5000 wind turbine at a range of 1850 m. This means that the scan proceeds along a horizontal axis 5 m above hub height of the 5 MW wind turbine through the rotor blades. For a better illustration the position of the wind turbines is marked in Figure 1. Multibrid M5000 is, as already mentioned before, located at a distance of 1850 m and at a width of 0 (M5000-1). The second wind turbine implied in Figure 2 at a range of 1850 m and approximately 200 m width is another wind turbine of the same type as Multibrid M5000 (M5000-2). The wind was blowing from southwest direction (compare Figure 1(b)). There can clearly be seen a velocity reduction in the wake of the wind turbines. After more detailed analysis it is found that this reduction is about 50 %. The length of the wake in this scan is more than six rotor diameters (one rotor diameter = 116 m). Besides the wakes of the two Multibrid wind turbines there can also be seen a smaller wake at a range of 2200 m and a width of about -150 m. This is the wake of another wind turbine in the measurement terrain which is of another type and can also be seen in Figure one. The measurement shown in

Figure 1: (a) Elevation scan in the wake of the Multibrid M5000. (b) Top view of azimuth scan.

(a) (b)

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Figure 2 was carried out during daytime and at a high level of turbulence. Because the atmospheric boundary layer is much more stable at night than during the day there were also done measurements after sunset to be able to distinguish between turbulence in the atmospheric boundary layer and turbulence induced by the wind turbine. Besides the measurements first trials were made to compare the data with the FLaP model [3].

Conclusions Successful field measurements of the ambient wind field of a multi-MW wind turbine were performed with a ground based long-range lidar. These measurements provide a good possibility for comparison with wake models. Acknowledgements This investigation is done in the framework of the project “LIDAR-Development of LIDAR technologies for the German offshore test field” of the German Federal Environment Ministry (BMU) (Contract No 0327642). Keywords: wake measurements, wind lidar, long range lidar, multi-MW wind turbine. References [1] Kopp, F.; Rahm, S. & Smalikho, I. Characterization of aircraft wake vortices by 2-mu m pulsed Doppler lidar Journal Of Atmospheric And Oceanic Technology, 2004, 21, 194-206 [2] Rahm, S.; Smalikho, I. & Kopp, F. Characterization of aircraft wake vortices by airborne coherent Doppler lidar Journal Of Aircraft, Amer Inst Aeronaut Astronaut, 2007, 44, 799-805 [3] Lange, B.; Waldl, H. P.; Guerrero, A. G.; Heinemann, D. & Barthelmie, R. J. Modelling of offshore wind turbine wakes with the wind farm program FLaP Wind Energy, John Wiley & Sons Ltd, 2003, 6, 87-104

Figure 2: Line of sight wind speed of an azimuth scan like illustrated in Figure 1(b) during daytime, depending on width and range.

Wind direction M5000-1

M5000-2

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Measurements of a multi-MW turbine near-wake using lidar from the nacelle

J.J. Trujillo1, F. Castellote2, O. Bischoff1, M. Hofsaess1,

D. Schlipf1, A. Rettenmeier1 and M. Kuehn1

1 Endowed Chair of Wind Energy at Universität Stuttgart Allmandring 5B, 70569 Stuttgart, Germany

Tel:+4968568289, Fax: +4968568293

2 Universidad Politécnica de Madrid, Spain

Corresponding author J.J. Trujillo

[email protected]

Abstract Lidar techniques are applied to measure wind fields in the near-wake of a 5 MW wind turbine. A commercial pulsed lidar has been adapted with flexible scanning capabilities to measure the wake wind field from the nacelle of the wind turbine. Simultaneous measurements are performed at several downstream positions in the range between half and two diameters downstream. Results of the analysis of dynamic and steady characteristics of the wind fields are shown under different operational conditions. Moreover, comparisons with an engineering near-wake model are performed. Introduction Advances in remote sensing techniques have shown lately a great potential for full field measurements relevant to the wind energy community. The light detection and ranging (lidar) technique is used here to measure the wind field in the wake of a multi-MW wind turbine. This type of system can measure wind fields in full scale in detail, in spatial and time domain, which is more extensive than with standard anemometry based on meteorological masts. Previous experiences in wake measurements have already been made with continuous wave (CW) lidar in far wake (at distances greater than two diameters downstream) [1]. Here a commercial pulsed lidar from the company Leosphere has been adapted with a flexible beam positioning system in order to scan the wake through different patterns. In contrast to CW-lidar systems, pulsed lidar systems are able to measure ‘simultaneously’ at different stations in the line-of-sight of the laser beam. This presents advantages to capture the large scale dynamics of the wake and the steady wake characteristics. The aim of these measurements is to capture the wind field in the region close to the rotor until two diameters downstream. The rotor induction plays an important role in the development of the wake at these distances. The obtained wind fields give insight into the processes affecting the wake aerodynamics in full field and serve for the validation of wake models. This extended abstract relates briefly the adaptations that have been made to the commercial lidar system, measured fields of wind speed and turbulence intensity and are

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compared to near-wake calculated as proposed by Madsen [2] compared to in the region close to the wind turbine rotor. Experiment setup Lidar scanner The lidar system used is a modified Windcube® which is manufactured by the French company Leosphere. It is a pulsed Doppler lidar with a 1.5µm wave length and a range gate of around 20m. The standard system is designed to measure vertical wind profiles up to around 200 m. The mirror/wedge used for the deviation of the beam to describe a conical domain has been changed by one mirror with two degrees of freedom where full control of the positioning is achieved. Additionally the internal configuration has been changed so that the beam is shooting from one side and not from the top. In this way a modular approach has been reached in that the scanner can be attached to the standard system without need of hardware modifications. On the software side, extensions have been made to synchronize the measurements with the mirror driving system. Two types of scanning procedure are distinguished, namely profiling and slicing. The first is used to produce horizontal or vertical profiles at a certain distance from the rotor. The second makes a surface (two-dimensional) scanning of the wind flow mainly perpendicular to the main flow direction. The present configuration permits to select maximum five stations in the line of sight with variable spacing. During one scanning cycle the system follows a desired path which is described by discrete points in space. The measurement takes place in a continuous mode with move-measure-move philosophy; a deceleration and immediate acceleration of the mirror driving system is performed when reaching a defined spatial ‘focus’ point. In this way the measurement (shooting plus calculations) begins just before reaching a defined point and ends after leaving the point with out stopping. This tries to ensure that the backscatter signal comes from a region as close as possible to the target focus point while performing a faster and smoother movement of the mirror. This scanning strategy provides a higher amount of focused points in time. Wind turbine The lidar scanner has been mounted on top of the nacelle of a 5MW Multibrid wind turbine at a level of around four meters above hub height and pointing backwards. The offshore prototype machine has 116m rotor diameter and 102m hub height. Moreover, it is fully equipped with sensors for loading and performance measurements which are used for the wind turbine certification. This provides data, such as the thrust and azimuth angles, which are important in determining the wake effects. Wind speed and direction data are obtained from a meteorological mast which is installed at two and a half rotor diameters in front of the turbine in the line of prevalent wind at the site. The mast is equipped with cup and sonic anemometers, and wind vanes at hub height. Simulation Simulation of the mean wind speed in the near-wake is compared to the measurements. The approach to model the near-wake is taken from the proposal by Madsen [2]. The rotor induction is calculated with the aeroelastic code FLEX5. Next it is assumed that the

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expansion of the wake takes place at two diameters downstream. The wind field between the rotor and this position is then estimated by conservation of mass. In this simplified approach the pressure gradients are neglected. Analyis of first results Measurements are being performed using slicing and vertical and horizontal profiling scanning modes. The first results lead us to the optimization of the scanning patterns. Two main aspects have been optimized; namely the scanning rate and the spatial density of focus points. The first has been accelerated by reducing the amount of averaged spectra for each focus point. This value has been taken from 10000, implemented in the standard in vertical profiler, down to 2000 with satisfactory backscatter signal most of the time, at least for the nearest stations with respect to the lidar source. This speeds up the calculation process and increases the amount of ‘focus’ points per time. The spatial density optimization is more exigent, it depends not only on the complexity of the flow but also on the type of scanning pattern selected. The near-wake presents a complex spatial structure, due to rotor induction, which is combined with operational effects like yaw, large scale turbulence, etc. This is more demanding especially for the slicing mode which spatial resolution is proportional to the focus point density. Slicing has been performed following a Lissajous trajectory which has been found adequate for far wake measurements through simulations. Moreover it is fast and smooth for the mirror drivers. Additionally horizontal profiling has been performed scanning an almost horizontal plane which intersects with hub height at a downstream distance of one diameter. The results show that for the slicing mode the measured wind fields are coarser and that details in the middle of the wake are not resolved as with a horizontal profiling which has more detail. This is due to the non-regularity of the distribution of focus points in a Lissajous trajectory, which tends to concentrate points in the outer part and leave a lower density in the middle of the scanned area. The results of these measurements are going to be presented along with comparisons of steady wind fields with the mentioned engineering model. Acknowledgements This investigation is done in the framework of the project "LIDAR - Development of LIDAR technologies for the German offshore test field" of The German Federal Environment Ministry (BMU) (Contract No 0327642). Keywords: near-wake, lidar, wake effects. References [1] Bingöl, F., Mann, J. Larsen, G.C., Light detection and ranging measurements of wake dynamics part I: one-dimensional scanning, Wind Energy, Published online 2009, doi: 10.1002/we.352. [2] Madsen, H. A.; Larsen, G. C.; Larsen, T. J.; Mikkelsen, R. & Troldborg, N. Wake deficit-and turbulence simulated with two models compared with inflow measurements on a 2MW turbine in wake conditions, In proceedings of EWEC, 2008.

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Meandering Wake and Porous Structure Models of Turbulent Wind Fields inside a Wind Farm

David Carruthers1, Amy Stidworthy1, Julian Hunt1,2 and Stephanie Gray1

Cambridge Environmental Research Consultants1

Centre for Polar Observation and Modelling, University College London2. Abstract As a component of the TOPFARM FP6 project, two complementary models of the turbulent wind field within and downstream of a wind farm are presented. Both models are fast to run and practical to use so that many scenarios taking account of different wind speeds and directions, turbine layouts and type etc. can be considered. The meandering wake model is based on a fluctuating plume model of Dyster el (2001). This model assumes that the wake meandering is determined by the turbulence external to the wake and takes account of the correlations in these larger scale flows in determining the interaction of the wakes of the different turbines. The porosity model is based on similar methodologies to those of Belcher et al (2003) and represents the wind farm as a distributed of forces. Each of the models are nested within a model for the turbulent flow of the atmospheric boundary layer over complex flow FLOWSTAR, (Carruthers et al 1988), allowing some considerations of the impacts of changes in surface elevation, surface roughness and stratification. Details of the models, example calculations and comparisons with field data will be presented. References Dyster SJ, Thompson DJ, McHugh CA and Carruthers DJ. (2001) Turbulent fluctuations and their use in estimating compliance standards and in model evaluation. International Journal of Environment and Pollution. Volume 16, Nos. 1-6. Belcher SE, Jerram N, and Hunt JCR. (2003) Adjustment of a turbulent boundary layer to a canopy of roughness elements. J Fluid Mech. Volume 488, 369-398. Carruthers DJ, Hunt JCR and Weng,W. (1988) Computational model of airflow over hills. FLOWSTAR I. Proceedings of Envirosoft. Computer Techniques in Environmental Studies, P. Zanetti, Ed., Springer Verlag.

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Status on development and validation of the dynamic wake meandering (DWM) model

T.J. Larsen, H. Aa. Madsen, G.C. Larsen, N. Troldborg, N. Johansen

Wind Energy Division

National Laboratory for Sustainable Energy Technical University of Denmark,

P.O. Box 49, 4000 Roskilde, Denmark

Corresponding author T.J.Larsen

[email protected] Abstract In this paper, the latest developments on the dynamic wake meandering (DWM) model is shortly described including comparisons to CFD simulations using the actuator line technique. The model is used to investigate the influence on turbine spacing on load and power production including variations in ambient turbulence levels. These results using the DWM model are compared to the Frandsen method1, where wake effects are included as an effective turbulence intensity. Since the first version of the dynamic wake meandering (DWM) model was presented in 20032,3,4, a number of developments of the model have been implemented. In the first versions of the DWM model the velocity deficit was computed with an external CFD based actuator disc model. However, recently5 the DWM model was fully integrated in the aeroelastic code HAWC2 by changing the computation of the velocity deficit to an engineering axis symmetric boundary layer equation (BLE) model, with the wake initial deficit derived from the blade element momentum (BEM) solution for the rotor induction. Added wake turbulence with smaller length scale than the ambient turbulence was also introduced in this version of the model. The latest development and tuning of submodels used in5 has been extensively described in6, in which the description in this paper can be considered a brief summary of. In the DWM model, three essential parts are conducted as illustrated in Figure 1. The first part is the calculation of the wake velocity deficit, which is carried out based on a combination between a classic blade element momentum method and a thin shear layer approximation of the Navier-Stokes equations in their rotational symmetric form. The second part is the inclusion of added wake turbulence, which is turbulence representing the contributions from mainly tip, root, trailed and shed vortices. As an illustration of the agreement between the DWM model and the CFD simulations using the actuator line technique7 (ACL) is shown in Figure 2. These deficits extracted in the wake of a turbine are based on full simulations including ambient turbulence and therefore gives a detailed insight in the performance of the full DWM model. A good agreement is seen for diameter distances 3, 6 and 10D and turbulence intensities of 5,10 and 15%.

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Figure1: Illustration of the main components in the DWM model.

Figure 2. Comparison of the DWM model with ACL results for the NM80 turbine at 8 m/s6, downstream positions of 3D, 6D and 10D (from left to right in the figure) and for 5%, 10% and 15%

ambient turbulence (from top to bottom). The non-dimensional axial velocities are shown. In order to investigated the influence on row spacing as well as ambient turbulence level, the DWM model has been used for full load simulations for a turbine placed behind an upstream turbine. The fatigue loads of selected sensors has been investigated and compared to similar results using the Frandsen method which is also the method recommended for wind turbine approvals. The influence on power production at 8m/s is shown in Figure 3 left, where a significant reduction is seen for close spacing. An interesting observation is the influence of ambient turbulence level which has a huge impact on the power production. When observing the fatigue loads of the longitudinal tower bottom bending moment a significant difference is seen between the DWM model and the Frandsen model. It is interesting to notice that the loads from the Frandsen method consistently decreases for increased turbine spacing, where the DWM results shows a maximum in loads at 6-8D. This is clearly a consequence of the meandering process which is also described in9. It is also interesting to see that the DWM model predicts very high tower loads for low ambient turbulence levels. In the IEC there is a discontinuity at 10D spacing which is a direct consequence of excluding wake turbulence for spacings larger than 10D.

Velocity Deficit Wake Added Turbulence Wake Meandering

Aeroelastic Simulation

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00.10.20.30.40.50.60.70.80.9

1

2 4 6 8 10 12 14 16 18 20

[-]

Distance [D]

Pe/Pe_free mean value

DWM TI 5%DWM TI 10%DWM TI 15%

0.5

1

1.5

2

2.5

3

3.5

4

4.5

2 4 6 8 10 12 14 16 18 20

[-]

Distance [D]

Tower bottom long. M_eq/M_eq_free 1Hz eq. value, m=3

DWM TI 5%DWM TI 10%DWM TI 15%

IEC TI 5%IEC TI 10%IEC TI 15%

Figure 3. Influence on power production in a full wake situation of a single turbine at a free wind speed of 8m/s. Left: power production normalized with the power output of a similar turbine in no wake (free) conditions. It is seen that power performance increases for increased spacing as well as

increased ambient turbulence. Right: 1 hz equivalent fatigue load for the tower bottom bending moment longitudinal using DWM and Frandsen method (IEC). The loads are normalized by the

fatigue loads at free conditions. A big difference is seen for low spacings and low ambient turbulence levels. A discontinuity is seen in the Frandsen loads at 10D spacing which is a direct consequence of

the exclusion of wake turbulence for spacings larger than 10D. Keywords: wake meandering, CFD, stochastic simulation, loads References 1 Frandsen, S.T. Turbulence and turbulence generated structural loading in wind turbine clusters. Risoe-R-1188(en). Risoe National laboratory of Denmark 2005. 2 Madsen, H.Aa., Thomsen, K. and Larsen, G.C. (2003). A New Method for Prediction of Detailed Wake Loads. IEA Annex XI Joint Action Meeting 16 on Aerodynamics of Wind Turbines, Boulder, U.S.A., May 5-6. 3 Thomsen, K.; Aagaard Madsen, H., A new simulation method for turbines in wake - applied to extreme response during operation. In: Proceedings. Special topic conference: The science of making torque from wind, Delft (NL), 19-21 Apr 2004. (Delft University of Technology, Delft, 2004) p. 425-432. 4 Thomsen, K.; Aagaard Madsen, H., A new simulation method for turbines in wake - Applied to extreme response during operation. Wind Energy (2005) 8, 35-47. 5 Madsen, H.A.; Larsen, G.C.; Larsen, T.J.; Mikkelsen, R.; Troldborg, N., Wake deficit-and turbulence simulated with two models compared with inflow measurements on a 2MW turbine in wake conditions. In: Scientific proceedings. 2008 European Wind Energy Conference and Exhibition, Brussels (BE), 31 Mar - 3 Apr 2008. (2008) p. 48-53. 6 Madsen, H.A.; Larsen,G.C.; Larsen, T.J.; Troldborg, N. Calibration and validation of the Dynamic Wake Meandering model implemented in the aeroelastic code HAWC2. Submitted to Journal of Solar Energy and Engineering. 7 Sørensen, J.N. and Shen, W.Z., 1999, ”Computation of Wind Turbine Wakes using Combined Navier Stokes/Actuator-line Methodology”, Proc. European Wind Energy Conference EWEC ’99, Nice. 8 Troldborg, N., Sørensen, J.N. and Mikkelsen, R., 2007, ”Actuator Line Simulation of Wake of Wind Turbine operating in Turbulent Inflow”, The Second Conference on The Science of making Torque from Wind. 28-31 August, Technical University of Denmark. J. Phys.: Conf. Ser. (2007) 75, 15 pp. 9 Larsen, T.J.; Larsen, G.C.; Aagaard Madsen, H.; Thomsen, K., Comparison of design methods for turbines in wake. Proc. 2008 European Wind Energy Conference and Exhibition, Brussels (BE), 31 Mar - 3 Apr 2008.

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A tailored eddy viscosity closure consistent with the Dynamic Wake Meandering philosophy

G.C. Larsen, H.Aa. Madsen and N. Troldborg

Wind Energy Division

Risø National Laboratory for Sustainable Energy Technical University of Denmark - DTU

P.O. Box 49, DK-4000 Roskilde, Denmark

Corresponding author G.C. Larsen

[email protected] Abstract The dynamic wake meandering (DWM) model [1] offers simple and fast modelling of wake flow fields which, for solitary wakes, has been verified by comparisons with full scale measurements of the wake flow field in e.g. [2] and [3]. The core of the DWM model is a split of scales in the wake flow field, with large scales being responsible for stochastic wake meandering, and small scales being responsible for wake attenuation and expansion in the meandering frame of reference as caused by (small scale) turbulent mixing. The wake deficit dynamics is thus essentially treated as a passive scalar controlled by the large scale turbulent structures in the atmospheric boundary layer (ABL). Noticing the free jet character of wake deficits, with the gradients of mean flow quantities being much bigger in radial direction than in axial direction, leads to a wake deficit formulation in the meandering frame of reference as based on the thin shear layer approximation of the Navier-Stokes equations. The formulation is further simplified by assuming rotationally symmetric wake deficits – an approximation that, for the far field characteristics, is supported by results from advanced LES CDF computations using an actuator line (ACL) approach [4]. Finally taking advantage of unsteady terms being described by the meandering mechanism, steady flow conditions are assumed in the meandering frame of reference, and the unsteady terms in the NS equations therefore discharged. To solve the resulting simple parabolic system a turbulence closure, expressing the Reynolds stresses in terms of the involved flow variables, is needed. This is the topic of the present paper. Basically, the relevant turbulent fluctuations refer to wake self generated turbulence and to ambient turbulence related to the ABL, respectively. Because these two turbulence contributions refer to fundamentally different processes, they may be considered as statistically independent. With this presumption the Reynolds stresses are decomposed into two linearly additive contributions associated with self generated- and ambient turbulence, respectively. Adopting the eddy viscosity concept, the eddy viscosity is in turn formulated as a sum of two contributions – one referring to the self induced wake turbulence, and the other referring to ambient atmospheric turbulence.

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We use the Boussinesq eddy viscosity approximation to obtain the Reynolds stress tensor as a product of an appropriate eddy viscosity and the mean strain rate tensor. For the present purpose, we will utilize both the original Boussinesq formulation, where the eddy viscosity is computed in terms of a suitable mixing length and a suitable mixing velocity, and Prandtl’s simplified version of this approach (i.e. Prandtl’s mixing length hypothesis [5]) with the mixing velocity expressed as a product of the mixing length and the relevant mean strain rate tensor. As for the ABL contribution, we postulate the mixing velocity to be proportional to an appropriate average of a characteristic radial turbulence component. To comply with the assumption of rotationally symmetry the averaging is defined as an azimuthally averaging operator. The closed form expression for resulting ABL contribution includes a specific dependence on turbulence intensities, turbulence length scales and on the degree of isotropy of the contributing turbulence components. Consistent with the DWM approach, the proposed turbulence closure further includes a suitable high pass filtering of the ABL turbulent scales contributing to the turbulent mixing of the wake deficit. As for the wake self generated contribution the traditional Prandtl’s mixing length formulation is applied. The eddy viscosity (and thereby the mixing length and the mixing velocity) is not an intrinsic property of the fluid but depends on the actual flow. Therefore, this quantity has to be calibrated to the type of flow in question. The proposed eddy viscosity formulation contains two free constants, and these are finally calibrated through comparisons with computational results from advanced LES CDF computations using the ACL approach. Keywords: Eddy viscosity, dynamic wake meandering (DWM), thin layer NS equations, wake deficits. References [1] G.C. Larsen et al. (2008). Wake meandering: A pragmatic approach. Wind Energy, 11,

377-395. [2] F. Bingöl, J. Mann and G.C. Larsen (2008). Lidar Measurements of Wake Dynamics

Part I: One Dimensional Scanning. Submitted for publication in Wind Energy. [3] H.Aa. Madsen, G.C. Larsen, T.J. Larsen and N. Troldborg (2009). Calibration and

validation of the Dynamic Wake Meandering model implemented in the aeroelastic code HAWC2. Submitted for publication in Journal of Solar Energy Engineering.

[4] N. Troldborg (2008). Actuator line modelling of wind turbine wakes. PhD dissertation, MEK-PhD 2008-03, DTU.

[5] L. Prandtl (1926). Ueber die ausgebildete Turbulenz, Proceedings of the Second International Congress for Applied Mechanics, Zürich, 12-17 September, pp. 62-74.

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A quasi 3D computation of multiple wakes using a boundary layer equation BLE model

H.Aa. Madsen, G.C. Larsen, N. Troldborg and T.J. Larsen

Wind Energy Division

Risø National Laboratory for Sustainable Energy Technical University of Denmark - DTU

P.O. Box 49, DK-4000 Roskilde, Denmark [email protected]

Corresponding author

H.Aa. Madsen [email protected]

Abstract In the dynamic wake meandering (DWM) model the meandering of the velocity deficit is the basic mechanism behind the increased loading in wake operation. The computation of the deficit is thus a crucial part of the model. In the first versions of the DWM model1 the velocity deficit was computed with an actuator disc model but in the later version2 where the DWM model was fully integrated in the aeroelastic code HAWC2, the velocity deficit was computed with an axis symmetric boundary layer equation (AS-BLE) model with the wake initial deficit derived from the blade element momentum (BEM) solution for the rotor induction. With this model complex (HAWC2 + AS-BLE model) it is possible to compute the velocity deficits for all the individual turbines in a row as shown in Figure 1 and thus also the array power losses3, shown in Figure 2, when the free wind is aligned with the row.

Figure 1 Inflow profiles to a row of turbines with a spacing of 10D.

Figure 2 Computed array losses for two spacings.

However, it is likewise important to extend the model complex to handle arbitrary wind directions to the row and also the interaction between different rows. The main concept in the extension of the present AS-BLE model to a quasy 3D BLE model is to use a 2D-BLE in the horizontal plane through the centre of the deficits and the AS-BLE model in vertical direction

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for each of the deficits. The two solutions are then coupled so that the centre velocity from the two models are equal for each individual deficit. The equations for the 2D-BLE model are the following:

2

2TU U UU Vx y y

ν∂ ∂ ∂+ =

∂ ∂ ∂ and 0U V

x y∂ ∂

+ =∂ ∂

and the eddy viscosity Tν

( )1 max minT b U Uν κ= − An example of computation of a single wake deficit with the 2D BLE model is shown in Figure 3 and the interaction of three deficits of different size is demonstrated in Figure 4.

Figure 3 Development of an initial rectangular deficit, computed with the 2D BLE model

Figure 4 Development of three deficits of different size, computed with the 2D BLE model

In the final paper the coupling of the two models will be considered and results on the interaction of two deficits will be compared with Actuator Line (AL) model results. Keywords: DWM model, wake deficits, wake meandering, boundary layer equation model, wake interaction. References 1 Thomsen, K.; Aagaard Madsen, H., A new simulation method for turbines in wake - Applied to extreme response during operation. Wind Energy (2005) 8 , 35-47. 2 Aagaard Madsen, H.; Larsen, G.C.; Larsen, T.J.; Mikkelsen, R.; Troldborg, N., Wake deficit-and turbulence simulated with two models compared with inflow measurements on a 2MW turbine in wake conditions. In: Scientific proceedings. 2008 European Wind Energy Conference and Exhibition, Brussels (BE), 31 Mar - 3 Apr 2008. (2008) p. 48-53. 3 Aagaard Madsen, H.; Larsen, G.C. and Larsen, T.J. “Development and calibration of an engineering model for simulation of wake velocity deficits” Presentation at IEA TASK 23 meeting: "Offshore Wind farms -Wake effects and Power Fluctuations", February 25, 2009, Risø DTU.

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Potential load reductions on megawatt turbines exposed to wakes using individual pitch wake compensator and trailing edge flaps

Helen Markou , Peter Bjørn Anderson

Risø National Laboratory, Roskilde, DK-4000, Denmark

[email protected]

Abstract. Wind turbines located in wind farms experience inflow wind conditions that are substantially modified compared to the ambient wind field that apply for stand-alone wind turbines due to upstream emitted wakes. This has implications not only for the power production of a wind farm, but also for the loading conditions of the individual turbines in the farm. The dynamic wake meandering model (DWM) [1] is believed to capture the essential physics of the wake problem, and thus both load and production aspects can be predicted, which is contrary to the traditional methods that typically focus on either load or power prediction. As a consequence the proposed formulation opens for control strategies for the individual turbine. Two control approaches for load reduction on the individual turbines are implemented in the multi-body aero-servo-elastic tool HAWC2, developed at Risø-DTU, and potential load reduction compared: a full blade ‘individual pitch controller’ acting as a wake compensator and a controller using trailing edge flaps. In the former implementation information on the wake deficit is extracted from pitot-tube measurements for the wake induced by one turbine [2], and the pitch angle of each blade is compensated for as an addition to the collective-pitch control. In the latter implementation a classical proportional and integral scalable controller has previously been designed in the ADAPWING2 project [3]. Combinations of 6.3 meter flap sections corresponding to 10% of the blade length, is placed at different radial blade positions. The flaps are allowed to operate independently of each other. This approach seems to offer high load reductions-potentially of the order of 60%. Keywords: Wind Turbine Control, Trailing edge flaps, Wake Model References [1] G.C. Larsen, et.al. (2008), ‘Wake meandering: A pragmatic approach’, Wind Energy 11, 377-395 [2] H.A. Madsen, G.C. Larsen, T.J. Larsen, ‘Wake deficit- and turbulence simulated with two models compared with inflow measurements on a 2MW turbine in wake conditions’, EWEC 2008. [3] ADAPWING2, T. Buhl, C. Bak, M. Gaunaa and P.B. Andersen, ‘Load Alleviation through Adaptive Trailing Edge Control Surfaces: ADAPWING Overview’, part of: Scientific proceedings, 2007, European Wind Energy Conference and Exhibition, EWEC 07, Milan.

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LES-simulation of a turbulent and meandering wake

Thomas Hahm, Steffen Wussow

F2E Fluid & Energy Engineering GmbH & Co. KG Borsteler Chaussee 178, D-22453 Hamburg, Germany

Phone: +49 40 55549081, Fax: +49 40 55549084

Corresponding author: Thomas Hahm

[email protected] Abstract The airflow around two wind turbines (WT) of the type ENERCON E66, hub height 65m, was simulated. The second WT is placed four rotor diameter behind the first WT and operates in its wake. The simulations were undertaken with the Computational Fluid Dynamics (CFD) software ANSYS FLUENT 6.3 using the LES technique for turbulence modelling. The incoming flow field was specified using a three component von-Karman turbulent wind model including wind shear. The geometry of the WTs includes tower, nacelle, rotating hub and blades. The wake inherently starts to meander during the simulation without using any further model assumptions. In contrast to our simulation of a single wake of the same WT in 2007 the computational grid has been further improved and the blades can be pitched during simulation. A comparison with data collected during a research project of the DIBt, which is the German authority responsible for WT type approval, shows, that the improved model captures the wake center deficit and the turbulence intensity at the measuring distance of 2.06 rotor diameter behind the WT in their full extent. Both these points have been shortcomings of the previous model. The comparison is based on time series of x-, y- and z-velocity at more than 50.000 locations inside the wake of the first WT, which were monitored at a rate of 10Hz during the simulations. This data might also be converted to input-files for BEM-based simulation tools to perform load calculations using realistic fully three-dimensional turbulent wakes.

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Keywords: wake meandering, CFD, LES. References Steffen Wußow, Thomas Hahm, Lars Sitzki (2007). 3D-simulation of the turbulent wake behind a wind turbine. In: The Science of Making Torque from Wind, Journal of Physics: Conference Series 75 (2007) 012033, p. 454- 459. Deutsches Institut für Bautechnik DIBt. Untersuchung des Nachlaufs von Windenergieanlagen und dessen Auswirkung auf die Standsicherheit der benachbarten WEA in Parkaufstellung; Forschungsvorhaben P 32-5-3.78-1007/02

Snapshot of the LES-Simulation showing contours of velocity magnitude ranging from 2m/s (blue) to 16m/s (red).

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Stochastic simulation of wake meander and turbulence in a wind farm

Morten Nielsen

Risø National Laboratory, Roskilde, DK-4000, Denmark

[email protected] Abstract This talk will present methods for simulation of turbulence inside wind farms. First a fluctuating horizontal 2D wind field in the wind-farm area is simulated. This dynamic field is then used for kinematic simulation of coherent meandering of all wakes in the wind farm. Wind fluctuations on the rotors of individual turbines are produced by combination of background turbulence, added wake turbulence, and wake velocity deficit. As a simplification, these conditions are assumed to be independent and the two latter ones are assumed to depend only on the varying centre-line position of the impinging wakes. The simulated wake meandering is therefore used to prescribe time-dependent turbulence parameters at various positions on the rotor-swept area. Random velocity time series at these positions are then simulated by a Fourier-based technique, which might be described as Veers’ method for unsteady turbulence1. The method is implemented in a program still under development and part of the ongoing EU TOPFARM project. The aim is to enable wind loads prediction as a function of turbine layout by methods fast enough to allow wind farm optimization. The plan for the stochastic turbulence simulation program is to works with mean flow fields from the WAsP Engineering2 program and to export simulated time series in a format compatible with existing aeroelastic turbine simulators. References 1 Nielsen, M.; Larsen, G.C.; Hansen, K.S., Simulation of inhomogeneous, non-stationary and non-Gaussian turbulent winds. International conference: The science of making torque from wind, Lyngby (DK), 28-31 Aug 2007. J. Phys.: Conf. Ser. (2007) 75 012060 doi: 10.1088/1742-6596/75/1/012060. 2 www.wasp.dk/Products/WEng.html

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Wake effects on turbine loading

Laust Olsen, Søren M. Pedersen

Siemens Wind Power A/S

Corresponding author Laust Olsen

Siemens Wind Power A/S Bourupvej 16, DK - 7330 Brande

Phone: +45 9942 8715 (direct) [email protected]

Abstract The wake meandering method as described by Risø/DTU has recently been implemented in aeroelastic design tools. The wind conditions for a turbine in wake are significant different from the wind field seen from a free wind turbine. The meandering wake model can be used for both wind farm power performance and design load calculations. The effective turbulence method is included in the IEC-61400-1 standard witch are the basis for the majority of installed wind farms today. Opposite the meandering model, which takes the main physical processes into account, the effective turbulence method is more empirical. The wake situations are covered just by increasing the turbulence intensity. On the other hand it is simple to apply in the design process. In fact it is considered to be important to apply models which reflect the real physical condition. This paper describes the adaptation of the filter settings in the meandering process. The meandering process is validated by measurement carried out at the Lillgrund offshore wind farm. Due to the layout of the wind farm two different down stream wake situations are investigated 3.3D and 4.8D respectively. The wind farm fatigue loads for a wind turbine in single wake during normal operation using the meandering model and using the effective turbulence intensity method proposed by S. Frandsen Risø/DTU are presented. The aeroelastic simulations using the two models are compared to each other and validated against measurements. The experimental setup at Lillgrund comprises both meteorological measurements as an intensive load instrumentation of blade, rotor and tower loads.

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Benchmarking of the Risø Dynamic Wake meandering model against CFD-AL calculations

Dick Veldkamp

Vestas Global Research Aero Systems, P.O. Box 63, 6990 AB Rheden, NETEHRLANDS

[email protected] Abstract Production of electricity from wind is done more and more in windfarms. This makes it important to have accurate models of wind turbine wakes, for prediction of both power and loads. A promising model was recently proposed by Risø, in which a wind speed deficit (precalculated with a variant of the Ainslie method), is moved back and forth over the rotor plane (Dynamic Wake Meandering model, DWM). The DWM is combined with conventional BEM calculations. Simultaneously another approach is being investigated at DTU: the CFD actuator line method (CFD-AL). Here CFD calculations on a coarse mesh are combined with any number of wind turbine structures. Speeds at the blade positions are extracted from the CFD calculations to work out forces and movements of the wind turbine structure. The forces found are in turn put onto the flow, creating realistic wind speed fields including wakes. In this paper results of the DWM/BEM model are compared to CFD-ACL for the case of a 80m diameter, 2.5 MW pitch-variable speed turbine. Parameters to be compared are: 1. Wind turbine power and loads in free stream 2. Wake shape and meandering of the wake centre 3. Wind turbine power and loads for operation in full wake and in half wake 4. Wind turbine power and loads in one wake and in multiple wakes. The idea of this paper is to provide independent verification of the model proposed by Risø.

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ACD modelling of wake interaction in Horns Rev wind farm

Stefan Ivanell1, Robert Mikkelsen2, Jens N Sørensen2, Dan Henningson3

1 Linné Flow Centre, KTH Mechanics, Stockholm, Sweden/Gotland University

2 Technical University of Denmark, Lyngby, Denmark 3 Linné Flow Centre, KTH Mechanics, Stockholm, Sweden

Abstract Large eddy simulations of the Navier-Stokes equations are performed to simulate the Horns Rev off shore wind farm 15 km outside the Danish west coast. The aim is to achieve a better understanding of the wake interaction inside the farm. The simulations are performed by combining the in-house developed computer code EllipSys3D with the actuator-disc methodology. In the actuator-disc method the blades are represented by a disc at which body forces representing the aerodynamic loading are introduced. The body forces are determined by computing local angles of attack and tabulated aerofoil coefficients. The advantage of using the actuator-disc technique is that it is not necessary to resolve blade boundary layers since the computational resources are devoted to simulating the dynamics of the flow structures. In the present study approximately 13.6 million mesh points are used to resolve the wake structure in the park. The park contains 80 wind turbines distributed over an area of about 20 km2. Since it is not possible to simulate all turbines, the 2 central columns of turbines have been simulated with periodic boundary conditions. This corresponds to an infinitely wide farm with 10 turbines in downstream direction. Simulations were performed within plus minus 15 degrees of the turbine alignment, making the wide farm approximation reasonable. The results from the CFD simulations are evaluated and the downstream evolution of the velocity field is depicted. Special interest is given to what extent the production is dependent on the inflow angle and turbulence level. The study shows that the applied method captures the main production variation within the wind farm. The result further demonstrates that levels of production correlate well with measurements. However, in some cases the variation of the measurement data is caused by variation of measurement conditions with inflow angles.

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Modelling the impact of wakes on power output in large offshore wind farms

R.J. Barthelmie 1,2, S.T. Frandsen2, O. Rathmann2, K. Hansen3, L.E. Jensen4,

S.Neckelmann5, W. Schlez6, J. Philips6, K. Rados7, J.G. Schepers8, E. Politis9, J. Prospathopoulos9, D. Cabezón10

1 Atmospheric Science Program and Center for Environmental Research, Indiana University,

USA ([email protected]) 2 Risoe DTU Laboratory for Sustainable Energy, Denmark

3 DTU, Denmark 4 DONG Energy, Denmark

5 Vattenfall, Denmark 6 Garrad Hassan and Partners, Germany/UK

7NTUA, Greece 8ECN, The Netherlands

9CRES, Greece 10CENER, Spain

Abstract The EU funded UPWind project brings together 40 partners working towards the design of very large wind turbines (8-10MW), both onshore and offshore. As part of this work, the research of our group is in flow and wakes in large wind farms in complex terrain and offshore. The first part of this work is to assess the state of the art in wake and flow modelling. We aim to radically improve wind farm models in order to improve power prediction and hence to continue to improve the costs of wind energy. Our group has access to a wide range of models from standard wind farm models used in industry, through to computational fluid dynamics (CFD) codes being evaluated for use in flow and wake modelling to new models being developed for improved modelling of large wind farm clusters. As data from the first large wind farms at Horns Rev and Nysted in Denmark were modeled, it became evident that standard approaches in wind farm models needed to be revaluated. Working through the Upwind project, specific case studies at Nysted and Horns Rev have been simulated with a range of wind farm and CFD models to improve wind farm modelling and address the issue of providing more accurate predictions of power output for wind farms in the planning stages. Our offshore data sets provided by DONG and Vattenfall comprise case studies at Horns Rev and Nysted. We focus on the prevailing westerly flow direction for a range of wind speed bands between 5 and 11 ms-1. For flow directly down the row at a very narrow angle, after the initial power drop due to wakes at the second turbine the subsequent power output tends to remain steady. However, if the angle is wider or the flow is not directly down the row, the power losses due to wakes continue to increase moving through the wind farm. Our model simulations are able to capture this behavior to some degree although the uncertainty bands on both models and data are large. We are now in the process of running

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identical simulations and data analysis at both Horns Rev and Nysted and these will be the focus of this paper. A further issue concerns the placement of multiple wind farm clusters such as Horns Rev 2 (under construction) and Nysted 2 (consented). The model challenge is to predict the ’interference’ of one wind farm on the power output of the next wind farm when separated by distances of less than 50 km. Current wind farm models tend to bring wind speeds to equilibrium too quickly in the offshore environment. An example of this is that after the coastal discontinuity the near surface wind speed profile attains its offshore equilibrium within 10-20 km of the coast whereas observations indicate that the adjustment of the wind speed profile occurs over much larger distances, approximately 50 km on average. This equilibrium distance is strongly dependent on wind speed and atmospheric stability. New models are being developed to encompass this range of challenges for wind farm power output prediction as wind farms become larger, developed in clusters or in complex topography. An alternative approach is to evaluate CFD models or to develop new parameterisations for existing models. We will describe some of the approaches being explored in UPWind and evaluate these in comparison with data from Nysted and Horns Rev.

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A wake flow model for large wind farms in inhomogeneous wind fields

Jochen Cleve

Siemens Wind Power A/S

E R WP EN 431, Dybendalsvænget 3, DK-2630 Taastrup Telefon: +45 44 77 49 89

[email protected] http://www.siemens.com/powergeneration

Abstract Most wake models have been developed for static and homogeneous wind fields. Average wind flows wich are used in applications like the layout of wind farms are described well by these wind wind fields. Nowadays wake models are often used in different circumstances, for example, advanced wind farm control and invetigations of power fluctuations. The time scales required for such applications are so short that the variability of the wind has to be taken into account in the models. For this purpose the Jensen model is extended to allow a wind field as input instead of a single wind vector. That is, the wind field is defined by a wind speed and direction at each turbine in the wind farm. The direction is given by calibrated turbine orientations and the wind speed is calculated from the wind measured at the upwind turbines of the farm. Each step of the generalisation is compared with the standard Jensen model and the implications are quantified.

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Development of a Large-eddy simulation (LES) model for modelling the far-wake effects of offshore windfarms

G. Steinfeld1, S. Raasch2, J. Tambke1, J. Peinke1 and D. Heinemann1

1 ForWind, Carl-von-Ossietzky Universität Oldenburg

Marie-Curie-Straße 1, 26129 Oldenburg, Germany Tel:+4944136116732, Fax: +4944136116739

2 Institut für Meteorologie und Klimatologie, Leibniz Universität Hannover Herrenhäuser Straße 2, 30419 Hannover, Germany

Corresponding author

G. Steinfeld [email protected]

Introduction to the RAVE-OWEA project The construction of Germany’s offshore wind energy test site “alpha ventus” (see fig. 1), situated in the North Sea 45 km north of the island of Borkum is seen as the starting point of large-scale exploitation of offshore wind resources in German waters. Therefore, Research at Alpha Ventus (RAVE) is funded by the German federal government. One of the joint research projects supported is entitled “Verification of Offshore Wind Turbines” (OWEA). It aims to verify essential aspects in the design and operation of offshore wind turbines by using the data of extensive measurements at the test site.

Fig. 1 Plan of the German offshore test site "alpha ventus"

Meteorological data has been recorded at FINO1 since September 2003. Two of the wind energy converters (4 and 7) at “alpha ventus” will be equipped with a horizontal scanning LIDAR system for upwind and downwind measurements of the wind velocity. Load and turbine data will be gained from four of the wind turbines (4, 5, 7 and 8). LIDAR and load measurements are expected to be available at the end of 2009.

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In addition numerical simulations using RANS as well as LES models are carried out that will be compared with each other and finally validated with data from the measurement campaigns. Due to their high spatial (RANS and LES) and temporal (LES) resolution those models will allow us a deeper insight into the flow conditions within wind farms as it would be possible from the measurements alone. Simulation of instationary flow conditions in offshore wind farms Work package 2 of the OWEA project, headed by ForWind Oldenburg, deals with the flow conditions inside wind farms and loading of wind turbines operating in wake of other turbines. Due to the lower intensity of turbulence in the marine boundary layer and due to the related persistency of wake turbulence, it expected that wake effects play a more important role for offshore than for onshore wind farms. Adjacent offshore wind farms can also decrease each other’s production and they modify the turbulent flow within the marine boundary layer considerably. These modifications are not well known, but the ambitious plans for offshore wind energy urgently require quantifications. ForWind applies the Parallelized Large-eddy simulation Model PALM (Raasch and Schröter, 2001) in order to study the flow field within and behind wind farms. The LES code PALM offers the possibility to prescribe an atmospheric turbulent inflow as well as to use cyclic boundary conditions. Thus, the turbulent flow within single wind farms as well as the interaction between adjacent wind farms can be efficiently simulated. While in our LES topography and the tower of a wind turbine can explicitly be resolved by using a modified version of the original mask method by Briscolini and Santangelo (1989) that is described in Letzel et al. (2008), the impact of the wind turbines on the flow is modelled by adding a sink term f to the equation of motion. Currently, we use the actuator disc approach either in the originally version proposed by Jimenez et al. (2007)

202

1 AuCf t−=

or in a version adjusted to the simulation of arrays of wind turbines by Meneveau (2009)

.1

121 2

−= rotort ua

ACf

Here, Ct denotes the thrust coefficient, a is the induction factor, A is the size of the rotor swept area, u0 is the undisturbed velocity at hub height, while urotor is the velocity directly at the rotor. Using several thousands of the CPUs of the HLRN (Norddeutscher Verbund zur Förderung des Hoch- und Höchstleistungsrechnen) SGI-ICE supercomputer allows us to simulate all parts of the marine atmospheric boundary layer with a very high resolution of up to 2 m, while at the same time model domains with horizontal extensions of several tens of square kilometres as required for the simulation of complete wind farms can be used. As a first validation of the modified version of PALM applied for the simulation of the wake flow downstream of wind turbines, a comparison with the numerical simulation and the measurements presented in Jimenez et al. (2007) have been carried out. The setup of our LES was kept similar to that of the LES in Jimenez et al. (2007), however, a considerably larger

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model domain has been used, e.g. in order to guarantee that the crosswise extension of the model domain amounts to four times the diameter of the largest turbulence elements that could be expected to be observed. The rotor diameter was 35 m instead of 30 m. Figure 2 shows the turbulence intensity and turbulent momentum flux observed 75 m behind the rotor disc, respectively. The results obtained with PALM are in good qualitative agreement with the values obtained from the measurements and the numerical simulation of Jimenez et al. (2007). However, there are still small quantitative differences such as an underestimation of the turbulence intensity of the vertical velocity component which might be related to the omittance of the rotation of the flow in the wake by the actuator disc method. Thus, in upcoming simulations we will use the actuator line method and investigate whether this method brings considerable benefits compared to the actuator disc method. Nevertheless, due to the encouraging qualitative agreement of the results with those in Jimenez et al. (2007) also first simulations of wake flows under offshore conditions have been carried out using the actuator disc method.

Fig. 2 Turbulent momentum flux and turbulence intensity plotted against wind direction.

Line: PALM; stars: LES Jimenez et al. (2007); circles: measurements Jimenez et al. (2007) Keywords: LES, marine boundary layer, offshore wind farm References Briscolini, M. and Santangelo, P. (1989). Development of the mask method for incompressible unsteady flows. J. Comput. Phys., 84, 57-75.

Jimenez, A., Crespo, A., Migoya, E. and Garcia, J. (2007). Advances in large-eddy simulation of a wind turbine wake. J. Phys. Conf. Series, 75, 012041.

Letzel, M.O., Krane, M. And Raasch, S. (2008). High resolution urban large-eddy simulation studies from street canyon to neighbourhood scale. Atmos. Env., 42, 8770-8774.

Meneveau, C. (2009). Wind turbine array fluid dynamics: measurements and modelling issues. Cornell workshop on large-scale wind generated power, Cornell University, Ithaca, New York, [online available under http://cfd.mae.cornell.edu/~caughey/WindPower_09/Presentations/Meneveau.pdf]

Raasch, S. and Schröter, M. (2001). A Large-Eddy Simulation Model performing on Massively Parallel Computers. Meteorol. Z., 10, 363-372.

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Modelling Very Large Wind Farms Offshore and Onshore

Wolfgang Schlez, Anja Neubert, Simon Cox

Garrad Hassan Deutschland GmbH, Garrad Hassan and Partners Ltd

Corresponding author Wolfgang Schlez

Garrad Hassan Deutschland GmbH, Marie-Curie-Str 1, 26129 Oldenburg, Germany Tel: +44 36116 880

[email protected] Abstract The typical size of wind farms has increased over the years and very large wind farms are reaching offshore and onshore 1000 and more turbines. New challenges have arisen from this to the modelling of wind farm effects. Past modelling efforts concentrated at modelling the effect of wind turbines typically over distances up to 20 Diameters downstream where individual wakes are strong. Wind farm designers today need models to be as accurate as possible over distances of up to 100 Diameters. Based on experiences and developments in the UPWIND project for offshore wind farms we present a model that is able to model large arrays of wind turbines onshore as well as offshore. This happens in a fast and computational efficient manner. The undisturbed flow is modeled by a suitable general flow model. The wind farm model is composed out of an empirical description of the near wake, a numerical RANS solver of the developing wake profile and a set of empirical approximations modelling the medium range disturbance (momentum deficit) to the atmospheric boundary layer caused by the presence of wind turbines. The model shows good results onshore and offshore. We present the model including validation cases from large onshore and offshore wind farms.

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A wind farm model in the context of distributed control of the wind farm

Arno J. Brand

ECN, P.O. Box 1, 1755 ZG Petten, Netherlands

Abstract In framework of the project FP7-ICT STREP 22548 / Aeolus, which is aimed at the development of distributed control of large offshore wind farms, maps of wind fields, mechanical loads and energy are developed. Such a map, which is to be part of the supervisory control algorithm, specifies in real time the wind speed at each turbine in a wind farm plus the tower bending moment, the blade bending moment, the rotor shaft torque and the aerodynamic power of each turbine as a function of "ambient" wind speed, wind direction and turbulence intensity. In this process the average as well as the standard deviation of each quantity is considered. First, the approach in the form of the dedicated wind farm model will be presented. Apart from the classic BEM-based sub-models, inspired by the rich literature on the topic, this wind farm model includes specially developed sub-models for the creation and the decay of velocity deficit, the creation and decay of added turbulence, the impact of turbulence on average values, and the standard deviation of all quantities. Next preliminary maps of wind, loads and energy as calculated with the wind farm model will be presented and be compared to measured information from e.g. the ECN Wind turbine Test site Wieringermeer EWTW.

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Prediction models for wind speed at turbines in a farm with application to control.

Torben Knudsen, Mohsen Soltani, Thomas Bak

Section of Automation and Control, Department of Electronic Systems, Aalborg University, Fredrik Bajersvej 7, DK-9220 Aalborg Ø, Denmark

Coresponding author:

Torben Knudsen [email protected]

(+45) 2787 9826 Abstract Introduction This paper describes the idea, approach, and preliminary results with prediction models for wind speed at turbines in a farm with application to control. This work is part of the EU-FP7 project with the title: Distributed Control of Large - Scale Offshore Wind Farms (Aeolus). The partners in the project are: Aalborg University Denmark, Industrial Systems and Control Ltd UK, Lund University Sweden, University of Zagreb Croatia, Energy research Centre of the Netherlands, Vestas Wind Systems A/S Denmark. Background The control of wind turbine farms can be separated in two levels. The controller serving the demands from the network operator gives a set point for active and reactive power for the whole farm. This set point can be the result of several operational modes: maximum energy production, rate limiting, balancing, frequency control, voltages control, or delta control. The Aeolus project focuses on the next level of the wind farm control. When the set point for the farm is given a strategy to control the individual turbines to achieve this demand is needed. Currently, this is done in a basic manner where all turbines essentially are treated the same disregarding the present local wind field and turbine status. The overall objective for the Aeolus project is: Given the total farm power reference: maximize energy production and/or minimize loads by coordinated control of individual turbines in a farm by exploiting the relation between turbines given by the common wind speed field. This is pursued by using the existing measurements on all the turbines. The control methods planned for this is centralized Model Predictive Control (MPC) and also decentralised control. In both methods it will be useful to have a Wind speed prediction method. Objectives for the wind speed prediction method 1. Investigate model structures useful for wind speed prediction in a farm. 2. Estimate parameters in the model structure from experimental data.

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3. Assess the prediction capability and the potentials for control. Tasks and methods Literature study. Obtaining relevant experimental data. Identification and estimation in classical input output Box Jenkins type of models and state space models. Development, identification and estimation it more specialized models. Assessing prediction error rms compare to standard deviation on wind speeds for prediction horizons relevant for the distances in a farm e.g. 1 minute.

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TOPFARM - A study on Wind Sector Management

Ingemar Carlén

Teknikgruppen AB , Box 2808 , 187 28 Täby , Sweden [email protected]

Abstract When developing large offshore wind farms, the issue of "optimal" wind farm control is today more often highlighted during the design phase. There are several different types of goals that can be identified when dealing with control concepts for wind farms. Work package 3 in the TOPFARM project is partly addressing a wind farm control option usually referred to as Wind Sector Management (WSM). Traditionally this means shutting down selected turbines in the farm in order to save fatigue life in case of narrow spacing and high levels of fatigue loading. In TOPFARM, the Wind Sector Management approach has been extended to include also derating of wind turbines, in order to facilitate wind farm design with a good balance between power production and fatigue loading. The ability to analyze WSM-controled wind farms where selected turbines are derated instead of shut down, is very much enhanced by a wind farm implementation of the Dynamic Wake Meandering model (DWM). Using the DWM-approach a realistic continuous variation of wake exposure for a chosen turbine can be modeled. This variation is mainly due to moderate wind direction changes in the "steady" atmospheric boundary layer flow, but is also caused by changes in axial momentum for upwind turbines due to wind speed fluctuations or blade pitching. The first phase of this work has mainly focused on two issues: A) How big is the potential for "continuous" WSM, and B) how can a master controller identify the degree of wake exposure for each individual turbine. The present study mainly treats the first issue above, and results from time simulations of small wind farms are presented. The next step will deal with the implementation and evaluation of a generalized controller concept.

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Wind farm optimization with structured and un-structured grids

Thomas Buhl, Ingemar Carlén and Gunner Larsen

Risø National Laboratory, Roskilde, DK-4000, Denmark [email protected]

Abstract Siting, developing and initial cost of large offshore wind turbine farms are typically an investment of seven or eight digits in euro. Traditionally, the topological layout of a wind turbine farm is made in a squared or rhomb grid. The orientation of the grid and the inter turbine spacing may at the best be optimized for power production. However, is this really optimal for power production and/or wear on the turbines? More versatile topological concepts may be advantageous, allowing parameters as e.g. initial cost of foundation to be taken into account, since it might be beneficial to avoid areas of certain water depths or certain soil conditions. The main issue in optimization of wind farms is the load and production consequences arising from wake deficits that significantly modify the wind farm wind climate compared to solitary wind turbines. The meandering wake deficits will thus lower the power production and increase the fatigue load damage on the turbines. In this paper we look at potential load reduction, potential initial cost reduction and potential production increase through optimization of the farm layout using structured and un-structured grids. Two optimization approaches are considered based on; a simple modeling of the wake effects through an engineering model combined with a very simple load cost model and a more time consuming approach, using an aeroelastic code including wake meandering, a BEM code and a beam element structural model. These optimizations are both carried out on un-structured grids with at least two design variables per turbine and with structured grids described in terms of a reduced number of design variables to reduce computational time.

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