Numerical Modeling of Wind Turbine Wakes

[+] Author and Article Information
Jens No̸rkær So̸rensen

Department of Mechanical Engineering, Building 403, Technical University of Denmark, DK-2800 Lyngby, Denmark

Wen Zhong Shen

Department of Mechanical Engineering, Building 403, Technical University of DenmarkAssociate Professor, Research Center for High Speed Trains, Changsha Railway University, China

J. Fluids Eng 124(2), 393-399 (May 28, 2002) (7 pages) doi:10.1115/1.1471361 History: Received November 16, 1999; Revised November 20, 2001; Online May 28, 2002
Copyright © 2002 by ASME
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Glauert, H., 1963, “Airplane Propellers,” Aerodynamic Theory, Durand, W. F., ed., Dover, New York.
Miller,  R. H., 1983, “The Aerodynamic and Dynamic Analysis of Horizontal Axis Wind Turbines,” J. Wind. Eng. Ind. Aerodyn., 15, pp. 329–340.
Simoes, F. J., and Graham, J. M. R., 1991, “Prediction of Loading on a Horizontal Axis Wind Turbine using a Free Vortex Wake Model,” Proc. 13th BWEA Wind Energy Conference, Quarton, D. C. and Fenton, V. C., eds., Mechanical Engineering Publications Limited, London, U.K., pp. 247–254.
Bareiss, R., and Wagner, S., 1993, “A Hybrid Wake Model for HAWT,” Proc. of the Sixth IEA Symposium on the Aerodynamics of Wind Turbines, McAnulty, K. F., ed., ETSU, Harwell, pp. 7.1–7.10.
Voutsinas,  S. G., Beleiss,  M. A., and Rados,  K. G., 1995, “Investigation of the Yawed Operation of Wind Turbines by Means of a Vortex Particle Method,” AGARD Conf. Proc., 552, pp. 11.1–11.11.
van Holten, Th., 1975, “The Computation of Aerodynamic Loads on Helicopter Blades in Forward Flight using the Method of the Acceleration Potential,” Report VTH-189, Dept. of Aerospace Eng., Delft Univ. of Techn., The Netherlands.
van Bussel, G. J. W., 1995, “The Aerodynamics of Horizontal Axis Wind Turbine Rotors Explored with Asymptotic Expansion Methods,” Doctoral dissertation, Technische Universiteit Delft, The Netherlands.
Wu,  T. Y., 1962, “Flow Through a Heavily Loaded Actuator Disc,” Schiffstechnik, 9, pp. 134–138.
Greenberg,  M. D., 1972, “Nonlinear Actuator Disc Theory,” Z. Flugwiss., 20 (3), pp. 90–98.
Conway,  J., 1995, “Analytical Solutions for the Actuator Disk with Variable Radial Distribution of Load,” J. Fluid Mech., 297, pp. 327–355.
Conway,  J., 1998, “Exact Actuator Disk Solution for Non-uniform Heavy Loading and Slipstream Contraction,” J. Fluid Mech., 365, pp. 235–267.
Sørensen,  J. N., and Myken,  A., 1992, “Unsteady Actuator Disc Model for Horizontal Axis Wind Turbines,” J. Wind. Eng. Ind. Aerodyn., 39, pp. 139–149.
Sørensen,  J. N., and Kock,  C. W., 1995, “A model for Unsteady Rotor Aerodynamics,” J. Wind. Eng. Ind. Aerodyn., 58, pp. 259–275.
Madsen, H. Aa., 1996, “A CFD Analysis for the Actuator Disc Flow Compared with Momentum Theory Results,” Proc. of the 10th IEA Symposium on the Aerodynamics of Wind Turbines, Pedersen, B. M., ed., Department of Fluid Mechanics, Technical University of Denmark, pp. 109–124.
Fejtek,  I., and Roberts,  L., 1992, “Navier-Stokes Computation of Wing/rotor Interaction for a Tilt Rotor in Hover,” AIAA J., 30 (11), pp. 2595–2603.
Rajagopalan, R. G., and Mathur, S. R., 1993, “Three Dimensional Analysis of a Rotor in Forward Flight,” J. Am. Helicopter Soc., 38 (3).
Sørensen,  J. N., Shen,  W. Z., and Munduate,  X., 1998, “Analysis of Wake States by a Full-field Actuator Disc Model,” Wind Energy, 1, pp. 73–88.
Sørensen, J. N., 1986, “Three-level, Viscous-inviscid Interaction Technique for the Prediction of Separated Flow Past Rotating Wings,” Ph.D. thesis, AFM Report 86-07, Department of Fluid Mechanics, The Technical University of Denmark.
Berkman, M. E., Sankar, L. N., Berezin, C. R., and Torok, M. S., 1997, “A Navier-Stokes/full potential/free wake Method for Rotor Flows,” AIAA Paper 97-0401.
Xu, G., and Sankar, L. N., 1999, “Computational Study of Horizontal Axis Wind Turbines,” AIAA Paper 99-0042.
Hansen, M. O. L., Sørensen, J. N., Michelsen, J. A., and Sørensen, N. N., 1997, “A Global Navier-Stokes Rotor Prediction Model,” AIAA Paper 97-0970.
Ekaterinaris, J. A., 1997, “Numerical Simulation of Incompressible Two-bladed Rotor Flow Field,” AIAA Paper 97-0398.
Duque, E. P. N., van Dam, C. P., and Hughes, S., 1999, “Navier-Stokes Simulations of the NREL Combined Experiment Phase II Rotor,” AIAA Paper 99-0037.
Sørensen, N. N., and Michelsen, J. A., 2000, “Aerodynamic Predictions for the Unsteady Aerodynamics Experiment Phase-II Rotor at the National Renewable Energy Laboratory,” AIAA Paper 2000–0037.
Huang,  Y., and Ghia,  U., 1992, “A Multigrid Method for Solution of Vorticity Velocity Form of 3-D Navier-Stokes Equations,” Commun. Appl. Numer. Methods, 8 (10), pp. 707–719.
Shen,  W. Z., and Ta Phouc,  L., 1997, “Numerical Method for Unsteady 3D Navier-Stokes Equations in Velocity-vorticity Form,” Comput. Fluids, 26, pp. 93–216.
Sørensen, J. N., Shen, W. Z., and Hansen, M. O. L., 2002, “A Vorticity-velocity Formulation of the 3D Navier-Stokes Equations in Cylindrical Coordinates,” Submitted.
Snel, H., Houwink, R., and Piers, W. J., 1993, “Sectional Prediction of 3D Effects for Separated Flow on Rotating Blades,” Proc. of the ECWEC ’93 Conference, pp. 395–399.
Chaviaropoulos,  P. K., and Hansen,  M. O. L., 2000, “Investigating Three-dimensional and Rotational Effects on Wind Turbine Blades by Means of a Quasi-3D Navier-Stokes Solver,” ASME J. Fluids Eng., 197, pp. 330–336.
Hoerner, S. F., 1965, Fluid-Dynamic Drag, published by the author.
Hansen, M. O. L., 1999, “Polar for NACA 63-415 Airfoil,” Report ET-AFM-9902, Department of Energy Engineering, Technical University of Denmark.
Abbott, I. H., and Doenhoff, A. E., 1959, Theory of Wing Sections, Dover Publications, New York.
Björck, A., 1996, “A Guide to Data Files from Wind Tunnel Test of a FFA-W3-211 Airfoil at FFA,” Technical Report FFA P-V-019, FFA, Bromma, Sweden.
Riegels, F. W., 1961, Aerofoil Sections, Butterworths, London.


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Staggered grid arrangement
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Cross section of computational domain
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Cross-sectional airfoil element
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Comparison of measured and computed mechanical power production for the Nordtank 500/41 wind turbine
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Comparison of force distributions computed on the original mesh (100×50×99) and on the fine mesh (150×50×148) at Vo=10 m/s
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Computed vorticity field showing the formation of the wake structure at Vo=10 m/s
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Distribution of axial interference factor, a=1−Vz/Vo, in the rotor plane at Vo=10 m/s
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Azimuthal distribution of axial interference factor, a, at Vo=10 m/s. Solid line: Distribution along r=70%R; Dashed line: Distribution along r=80%R
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Radial distributions of averaged interference factors ā(r) and ā(r), defined in Eqs. (161718), computed at Vo=10 m/s
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Distribution of axial velocity for Vo=10 m/s. The core of the tip vortices are marked by •



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