Development of a new free wake model using finite vortex element for a horizontal axis wind turbine

  • Shin, Hyungki (Korea Institute of Energy Research) ;
  • Park, Jiwoong (Doosan Heavy Industries & Construction) ;
  • Lee, Soogab (School of Mechanical and Aerospace Engineering, Seoul National University)
  • Received : 2016.03.28
  • Accepted : 2017.01.15
  • Published : 2017.03.30


The treatment of rotor wake has been a critical issue in the field of the rotor aerodynamics. This paper presents a new free wake model for the unsteady analysis for a wind turbine. A blade-wake-tower interaction is major source of unsteady aerodynamic loading and noise on the wind turbine. However, this interaction can not be considered in conventional free wake model. Thus, the free wake model named Finite Vortex Element (FVE hereafter) was devised in order to consider the interaction effects. In this new free wake model, the wake-tower interaction was described by dividing one vortex filament into two vortex filaments, when the vortex filament collided with a tower. Each divided vortex filaments were remodeled to make vortex ring and horseshoe vortex to satisfy Kelvin's circulation theorem and Helmholtz's vortex theorem. This model was then used to predict aerodynamic load and wake geometry for the horizontal axis wind turbine. The results of the FVE model were compared with those of the conventional free wake model and the experimental results of SNU wind tunnel test and NREL wind tunnel test under various inflow velocity and yaw condition. The result of the FVE model showed better correlation with experimental data. It was certain that the tower interaction has a strong effect on the unsteady aerodynamic load of blades. Thus, the tower interaction needs to be taken into account for the unsteady load prediction. As a result, this research shows a potential of the FVE for an efficient and versatile numerical tool for unsteady loading analysis of a wind turbine.


Supported by : Korea Institute of Energy Research (KIER), Korea Institute of Energy Technology Evaluation and Planning (KETEP)


  1. Hansen, K. S., Barthelmie, R. J., Jensen, L. E. and Sommer, A., "The Impact of Turbulence Intensity and Atmospheric Stability on Power Deficits due to Wind Turbine Wakes at Horns Rev Wind Farm", Wind Energy, Vol. 15, 2012, pp. 183-196.
  2. Gaumond, M., Rethore, P. E., Bechmann, A., Ott, S., Larsen, G. C., Pena Diaz, A. and Kurt, K. S., "Benchmarking of Wind Turbine Wake Models in Large Offshore Wind Farms", The Science of Making Torque from Wind, Oldenburg, 2012.
  3. Hansen, A. V. and Butterfield, C. P., "Aerodynamics of Horizontal-Axis Wind Turbines", Annual Review of Fluid Mechanics, Vol. 25, 1993, pp. 115-149.
  4. Duque, E. P. N., Van Dam, C. P. and Hughes, S. C., "Navier-Stokes Simulations of the NREL Combined Experiment Phase II Rotor", European Wind Energy Conference, Nice, France, 1999.
  5. Montgomerie, B., "The Need for more Measurements", Proceedings of the 4th International Energy Agency(IEA) Aerodynamics Symposium, Rome, Italy, 1990.
  6. Whale, J., Anderson, C. G., Bareiss, R. and Wagner, S., "An Experimental and Numerical Study of the Vortex Structure in the Wake of a Wind Turbine", Journal of Wind Engineering and Industrial Aerodynamics, Vol. 84, 2000, pp. 1-21.
  7. Leishman, J. G., "Challenges in Modelling the Unsteady Aerodynamics of Wind Turbines", Wind energy, Vol. 5, 2002, pp. 85-132.
  8. Coton, N. F., Wang, T. and Galbraith, R. A. McD., "An Examination of Key Aerodynamic Modelling Issues Raised by the NREL Blind Comparison", Wind Energy, Vol.5, 2003, pp. 199-212.
  9. Chaderjian, M. N., "Advances in Rotor Performance and Turbulent Wake Simulation using DES and Adaptive Mesh Refinement", Seventh International Conference on Computational Fluid Dynamics (ICCFD7), Big Island, Hawaii, 2012.
  10. Cottet, G. H. and Koumoutsakos P., Vortex Methods: Theory and Practice, Cambridge University Press, New York, 2000.
  11. Van Heemst, J. W., Baldacchino, D., Metha, D. and Van Bussel, G. J. W., "Coupling of a Free Wake Vortex Ring Near-wake Model with Jensen and Larsen Far-wake Deficit Models", Wake Conference, Gotland, Sweden, 2015
  12. Sanderse, B.,"Aerodynamics of Wind Turbine Wakes Literature Review", ECN Technical Report ECN-e-09-016.
  13. Vermeer, L. J., Sorensen, J. N. and Crespo, A., "Wind Turbine Wake Aerodynamics", Progress in Aerospace Sciences, Vol. 39, 2003, pp. 467-510.
  14. Zhang, W., Markfort, C. D. and Porte-Agel, F., "Nearwake Flow Structure Downwind of a Wind Turbine in a Turbulent Boundary Layer", Experiments in Fluids, Vol. 52, 2012, pp. 1219-1235.
  15. Bastankhah, M. and Porte-Agel, F., "A New Analytical Model for Wind-Turbine Wakes", Renewable Energy, Vol. 70, 2014, pp. 116-123.
  16. Kim, H., Lee, S. and Lee, S., "Influence of Blade-tower Interaction in Upwind-type Horizontal Axis Wind Turbines on Aerodynamics", Journal of Fluid Science and Technology, Vol. 25, No. 5, 2011, pp. 1351-1360.
  17. Park, J., "Experimental Study about Performance and Wake Structure of the Wind Turbine Blade", A Master's Thesis, Seoul National University, 2005.
  18. Simms, D., Schreck, S., Hand, M. and Fingersh, L. J., "NREL Unsteady Aerodynamics Experiment in the NASA-Ames Wind Tunnel : A Comparison of Predictions to Measurements", NREL/TP-500-29494, 2001.
  19. Kao, D., Ahmad, J., Holst, T., Brian, G. and Allan, B., "Visualization and Analysis of Vortex Features in Helicopter Rotor Wakes", 51st AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition, Texas, 2013.
  20. Bliss, D. B., Quackenbush, T. R. and Bilanin, A. J., "A New Methodology for Helicopter Free Wake Analyses", 39th Annual Forum of the American Helicopter Society, St. Louis, MO, 1983.
  21. ABEDI, H., "Development of Vortex Filament Method for Aerodynamic Loads on Rotor Blades", Thesis for the Degree of Licentiate of Engineering, Chalmers University of Technology, 2013.
  22. McCroskey, W. J., "Vortex Wakes of Rotorcraft", 33rd Aerospace Sciences Meeting and Exhibit, Reno, NV, 1995.
  23. Shin, H., Park, J. and Lee, S., "A New Free Wake Model Development for Simulation of Wind Turbine Performance", World Wind Energy Conference, Beijing, China, 2004.
  24. Quackenbush, T. R., Bliss, D. B., Wachspress, D. A. and Ong, C. C., "Free-Wake Analysis of Hover Performance Using a New Influence Coefficient Method", NASA CR 4309, 1990.
  25. Corrigan, J. J. and Schilling, J. J., "Empirical Model for Stall Delay Due to Rotation", American Helicopter Society Aeromechanics Specialists Conference, San Francisco, CA, 1994.
  26. Tangler, J. L. and Selig, M. S., "An Evaluation of an Empirical Model for Stall Delay due to Rotation for HAWTS", Windpower '97, Austin, Texas, 1997.
  27. Du, Z. and Selig, M. S., "A 3-D Stall-Delay Model for Horizontal Axis Wind Turbine Performance Prediction", ASME Wind Energy Symposium, Reno, NV, 1998.