Effect of Transitional Turbulence Modelling on a Straight Blade Vertical Axis Wind Turbine

Part of the Advanced Structured Materials book series (STRUCTMAT, volume 34)


The flow around straight blade vertical axis wind turbines is typically complex at low tip speed ratios (TSR < 2). In this paper, the turbulence models which are based on the assumption of fully developed turbulent flow, such as S-A, RNG κ-ε and SST κ-ω have been investigated in comparison to the SST transitional model (both with and without curvature correction) to account for the laminar-turbulence transition. The investigation is based on the 2D unsteady Reynolds averaged Navier–Stokes (URANS) equations using a sliding mesh technique. It has been found that applying turbulence models based on the assumption of fully developed flow shows significant differences in velocity magnitude if the flow is under stall condition or wake effect compared to the transitional model. Also, the predicted flow structure in the vicinity of the stalled airfoils using different types of turbulence models is found to be different compared to the un-stalled airfoils where no significant differences in the flow field have been observed. In the wake region, the flow varies less significantly compared to the stalled airfoils.


Wind Turbine Azimuthal Angle Curvature Correction Stream Line Shear Stress Transport 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



Khaled M. Almohammadi would like to express his gratitude to Taibah University, Kingdom of Saudi Arabia for supporting him to perform his PhD study in the University of Leeds.


  1. 1.
    Wang, S., Ingham, D.B., Ma, L., Pourkashanian, M., Tao, Z.: Numerical investigations on dynamic stall of low Reynolds number flow around oscillating airfoils. Comput. Fluids 39, 1529–1541 (2010)CrossRefzbMATHGoogle Scholar
  2. 2.
    Paraschivoiu, I.: Wind Turbine Design: With Emphasis on Darrieus Concept. Polytechnic International Press, Canada (2002)Google Scholar
  3. 3.
    Sharpe, D.: A theoretical and experimental study of the Darrieus vertical axis wind turbine. Polytechnic School of Mechanical, Aeronautical and Production Engineering (1977)Google Scholar
  4. 4.
    Holme, O.: A contribution to the aerodynamic theory of the vertical-axis wind turbine. In: International Symposium on Wind Energy Systems, Cambridge, England, pp. C4-55–C4-71 (1976)Google Scholar
  5. 5.
    Strickland, J.: A performance prediction model for the Darrieus turbine. In: International Symposium on Wind Energy Systems, Cambridge, UK, pp. C3-39–C3-54 (1976)Google Scholar
  6. 6.
    Bergey, K.: The lanchester-betz limit. J. Energy 3, 382–384 (1979)CrossRefGoogle Scholar
  7. 7.
    Mathew, S.: Wind Energy: Fundamentals, Resource Analysis and Economics. Springer, Berlin (2006)CrossRefGoogle Scholar
  8. 8.
    Lv, Y.Z., Jiang, D.X., Jiang, Y.: Numerical simulation on small scale straight-blade and twisted-blade vertical axis wind turbine. Adv. Mater. Res. 455, 334–338 (2012)Google Scholar
  9. 9.
    Anderson, J., Wendt, J.: Computational Fluid Dynamics. McGraw-Hill, New York (1995)Google Scholar
  10. 10.
    Versteeg, H., Malalasekera, W.: An Introduction to Computational Fluid Dynamics: The Finite Volume Method. Prentice Hall, NJ (2007)Google Scholar
  11. 11.
    Tu, J., Yeoh, G.H., Liu, C.: Computational Fluid Dynamics: A Practical Approach, 1st edn. Butterworth-Heinemann, Burlington (2008)Google Scholar
  12. 12.
    Islam, M., Amin, M., Carriveau, R., Fartaj, A.: Investigation of low reynolds number airfoils for fixed-pitch straight-bladed VAWT, pp. 5–8Google Scholar
  13. 13.
    Islam, M., Ting, D., Fartaj, A.: Aerodynamic models for Darrieus-type straight-bladed vertical axis wind turbines. Renew. Sustain. Energy Rev. 12, 1087–1109 (2008)CrossRefGoogle Scholar
  14. 14.
    Hinze, J.: Turbulence, vol. 13, pp. 741–773. McGraw Hill Book Company, NY (1975)Google Scholar
  15. 15.
    Launder, B., Spalding, D.: Lectures in Mathematical Models of Turbulence. Academic Press, NY (1979)Google Scholar
  16. 16.
    Spalart, P.R., Allmaras, S.R.: A one-equation turbulence model for aerodynamic flows. La recherche aérospatiale 1, 5–21 (1994)Google Scholar
  17. 17.
    Yakhot, V., Orszag, S., Thangam, S., Gatski, T., Speziale, C.: Development of turbulence models for shear flows by a double expansion technique. Phys. Fluids A 4, 1510 (1992)CrossRefzbMATHMathSciNetGoogle Scholar
  18. 18.
    Menter, F.R.: Two-equation eddy-viscosity turbulence models for engineering applications. AIAA J. 32, 1598–1605 (1994)CrossRefGoogle Scholar
  19. 19.
    Reynolds, O.: On the dynamical theory of turbulent incompressible viscous fluids and the determination of the criterion. Phil. Trans. R. Soc. 186, 123–161 (1895)Google Scholar
  20. 20.
    Jackson, D., Launder, B.: Osborne Reynolds and the publication of his papers on turbulent flow. Fluid Mech. 39, 19–35 (2007)CrossRefMathSciNetGoogle Scholar
  21. 21.
    Papageorgakis, G., Assanis, D.N.: Comparison of linear and nonlinear RNG-based k-epsilon models for incompressible turbulent flows. Numer. Heat Transf. Part B Fundam. 35, 1–22 (1999)CrossRefGoogle Scholar
  22. 22.
    Baldwin, B., Lomax, H.: Thin Layer Approximation and Algebraic Model for Separated Turbulent Flows. AIAA Paper, U.S., pp. 78–257 (1978)Google Scholar
  23. 23.
    Kato, M., Launder, B.: Three-dimensional modelling and heat-loss effects on turbulent flow in a nominally two-dimensional cavity. Int. J. Heat Fluid Flow 16, 171–177 (1993)Google Scholar
  24. 24.
    Ince, N., Launder, B.: Three-dimensional and heat-loss effects on turbulent flow in a nominally two-dimensional cavity. Int. J. Heat Fluid Flow 16, 171–177 (1995)CrossRefGoogle Scholar
  25. 25.
    Wilcox, D.: Turbulence Modeling for CFD. DCW Industries, Inc., CA (1993)Google Scholar
  26. 26.
    Menter, F., Kuntz, M., Langtry, R.: Ten years of industrial experience with the SST turbulence model. Turbul. Heat Mass Transf. 4, 2003 (2003)Google Scholar
  27. 27.
    Menter, F.R.: Review of the shear-stress transport turbulence model experience from an industrial perspective. Int. J. Comput. Fluid Dyn. 23, 305–316 (2009)CrossRefzbMATHGoogle Scholar
  28. 28.
    Langtry, R., Menter, F., Likki, S., Suzen, Y., Huang, P., Völker, S.: A correlation-based transition model using local variables—Part II: Test cases and industrial applications. J. Turbomach. 128, 423 (2006)CrossRefGoogle Scholar
  29. 29.
    Menter, F., Langtry, R., Likki, S., Suzen, Y., Huang, P., Völker, S.: A correlation-based transition model using local variables—Part I: Model formulation. J. Turbomach. 128, 413 (2006)CrossRefGoogle Scholar
  30. 30.
    Wang, S., Ma, L., Ingham, D.B., Pourkashanian, M., Tao, Z.: Turbulence modelling of deep dynamic stall at low Reynolds number. Lect. Notes Eng. Comput. Sci. 2, 184 (2010)CrossRefGoogle Scholar
  31. 31.
    Genç, M.S., Karasu, I., Açıkel, H.H., Akpolat, M.T.: An experimental study on aerodynamics of NACA2415 aerofoil at low Re numbers. Exp. Thermal Fluid Sci. 39, 252–264 (2012)Google Scholar
  32. 32.
    White, F.M.: Viscous Fluid Flow, vol. 2. McGraw-Hill, New York (1991)Google Scholar
  33. 33.
    Cebeci, T., Mosinskis, G.J., Smith, A.M.O.: Calculation of separation points in incompressible turbulent flows. J. Aircraft 9, 618–624 (1972)CrossRefGoogle Scholar
  34. 34.
    Drela, M., Giles, M.: Viscous-inviscid analysis of transonic and low Reynolds number airfoils. AIAA J. 25, 1347–1355 (1987)CrossRefzbMATHGoogle Scholar
  35. 35.
    Lian, Y., Shyy, W.: Laminar-turbulent transition of a low Reynolds number rigid or flexible airfoii. AIAA J. 45, 1501–1513 (2007)CrossRefGoogle Scholar
  36. 36.
    Walters, D.K., Leylek, J.H.: Computational fluid dynamics study of wake-induced transition on a compressor-like flat plate. J. Turbomach. 127, 52–63 (2005)CrossRefGoogle Scholar
  37. 37.
    Cutrone, L., De Palma, P., Pascazio, G., Napolitano, M.: Predicting transition in two-and three-dimensional separated flows. Int. J. Heat Fluid Flow 29, 504–526 (2008)CrossRefGoogle Scholar
  38. 38.
    Nakamori, I., Ikohagi, T.: Dynamic hybridization of MILES and RANS for predicting airfoil stall. Comput. Fluids 37, 161–169 (2008)CrossRefzbMATHGoogle Scholar
  39. 39.
    Abu-Ghannam, B., Shaw, R.: Natural transition of boundary layers—the effects of turbulence, pressure gradient, and flow history. J. Mech. Eng. Sci. 22, 213–228 (1980)CrossRefGoogle Scholar
  40. 40.
    Sørensen, N.N.: CFD modelling of laminar-turbulent transition for airfoils and rotors using the γ-model. Wind Energy 12, 715–733 (2009)CrossRefGoogle Scholar
  41. 41.
    Durbin, P.: Near-wall turbulence closure modelling without “damping functions”. Theoret. Comput. Fluid Dyn. 3, 1–13 (1991)zbMATHGoogle Scholar
  42. 42.
    Benini, E., Ponza, R.: Laminar to turbulent boundary layer transition investigation on a supercritical airfoil using the γ − θ transitional model. In: 40th Fluid Dynamics Conference and Exhibit, Chicago, Illinois, p. 4289 (2010)Google Scholar
  43. 43.
    Castelli, M.R., Garbo, F., Benini, E.: Numerical investigation of laminar to turbulent boundary layer transition on a Naca 0012 airfoil for vertical-axis wind turbine applications. Wind Eng. 35, 661–686 (2011)CrossRefGoogle Scholar
  44. 44.
    Wang, S., Ingham, D.B., Ma, L., Pourkashanian, M., Tao, Z.: Turbulence modelling of deep dynamic stall at relatively low Reynolds number. J. Fluids Struct. 33, 191–209 (2012)CrossRefGoogle Scholar
  45. 45.
    Almohammadi, K.M., Ingham, D.B., Ma, L., Pourkashanian, M.: CFD sensitivity analysis of a straight-blade vertical axis wind turbine. Wind Eng. 5, 571 (2012)CrossRefGoogle Scholar
  46. 46.
    Kooiman, S., Tullis, S.: Response of a vertical axis wind turbine to time varying wind conditions found within the urban environment. Wind Eng. 34, 389–401 (2010)Google Scholar
  47. 47.
    Bravo, R., Tullis, S., Ziada, S.: Performance testing of a small vertical-axis wind turbine. In: 21st Canadian Congress of Applied Mechanics, Toronto, Ontario, Canada (2007)Google Scholar
  48. 48.
    McLaren, K.W.: A numerical and experimental study of unsteady loading of high solidity vertical axis wind turbines. Phd, Mechanical Engineering, McMaster University, McMaster (2011)Google Scholar
  49. 49.
    Almohammadi, K.M., Ingham, D., Ma, L., Pourkashanian, M.: CFD modelling investigation of a straight-blade vertical axis wind turbine. In: Presented at the 13th International Conference on Wind Engineering, Amsterdam, Netherland (2011)Google Scholar
  50. 50.
    Ferreira, C.S., Bijl, H., van Bussel, G., van Kuik, G.: Simulating dynamic stall in a 2D VAWT: Modeling strategy, verification and validation with particle image velocimetry data. J. Phys: Conf. Ser. p. 012023 (2007)Google Scholar
  51. 51.
    Camporeale, S.M., Magi, V.: Streamtube model for analysis of vertical axis variable pitch turbine for marine currents energy conversion. Energy Convers. Manage. 41, 1811–1827 (2000)CrossRefGoogle Scholar
  52. 52.
    McLaren, K., Tullis, S., Ziada, S.: Computational fluid dynamics simulation of the aerodynamics of a high solidity, small-scale vertical axis wind turbine. Wind Energy 15, 349–361 (2011)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.CFD Centre, ETII, Faculty of EngineeringUniversity of LeedsLeedsUK
  2. 2.Mechanical Engineering, Taibah UniversityMadinahSaudi Arabia
  3. 3.CFD Centre, ETII, Faculty of EngineeringUniversity of LeedsLeedsUK

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