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Wind Turbine Aerodynamics and Vorticity-Based Methods pp 299–306Cite as

Yaw-Modelling Using a Skewed Vortex Cylinder

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Part of the book series: Research Topics in Wind Energy ((RTWE,volume 7))

Abstract

The cylindrical vortex wake model presented in Chap. 17 for the case of uniform inflow is extended in the current chapter to the case of yawed inflow. Generalities regarding yaw are presented in Sect. 6.1 and only the skewed cylindrical vortex model is presented in this chapter. The chapter starts with a literature review on the topic of yaw-models and vorticity-based methods. The description of the model follows. The novelty of the current model is that the assumption of infinite tip-speed ratio is relaxed. The bound vorticity is assumed to be identical to the case of uniform inflow but the vortex cylinder and the root vortex are skewed with respect to the normal of the rotor disk. Closed form formulae for the induced velocities are provided. They can only be evaluated analytically for a limited part of the domain. A numerical integration is required to obtain the velocity everywhere in the domain. The numerical integration poses no difficulty for modern computers. Semi-empirical models are established to obtain the velocity at the rotor disk. The contribution from each vorticity components to the induced velocity at the rotor disk is investigated. The content of this chapter is based on the publication of the author titled “Cylindrical vortex wake model: skewed cylinder, application to yawed or tilted rotors” (Branlard, Gaunaa, Wind Energy, 2015,  [1]). Details on the mathematical derivations used in this chapter are provided in Chap. 38. Results from this chapter are applied in Chap. 22 to derive a new yaw-model applicable to a BEM code. The induction zone in front of a yawed wind turbine or rotor is investigated in Chap. 24 based on the results from the current chapter. A Matlab source code to evaluate the induced velocity field in the entire domain due to the main vorticity component is provided in Sect. 38.1.4.

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Notes

  1. 1.

    The derivations are detailed in Chap. 38.

  2. 2.

    The relation \(h-\lambda \) presented here is a simplified measure for qualitative assessment. It uses the axial induction at the rotor and \(a'=0\) to assess the pitch, instead of a more correct formulation that would consider the far-wake induction.

References

  1. E. Branlard, M. Gaunaa, Cylindrical vortex wake model: skewed cylinder, application to yawed or tilted rotors. Wind Energy (2015). page (Online)

    Google Scholar 

  2. T. Burton, D. Sharpe, N. Jenkins, E. Bossanyi, Wind Energy Handbook, 1st edn. (Wiley, New-York, 2002)

    Google Scholar 

  3. W. Castles, J.H. De Leeuw, The normal component of the induced velocity in the vicinity of a lifting rotor and some examples of its application. Technical report, NACA Report No. 1184, Giorgia Institute of Technology, Atlanta (1954)

    Google Scholar 

  4. W. Castles, H.L. Durham, Distribution of normal component of induced velocity in lateral plane of a lifting rotor. Technical report, NACA TN-3841 (1956)

    Google Scholar 

  5. K. Chaney, A.J. Eggers, Expanding wake induction effects on thrust distribution on a rotor disc. Wind Energy 5, 213–226 (2002)

    Article  Google Scholar 

  6. K. Chaney, A.J. Eggers, P.J. Moriarty, W.E. Holley, Skewed wake induction effects on thrust distribution on small wind turbine rotors. J. Sol. Energy Eng. 123(4), 290–295 (2001)

    Article  Google Scholar 

  7. R.P. Coleman, A.M. Feingold, C.W. Stempin, Evaluation of the induced-velocity field of an idealized helicopter rotor. NACA ARR No. L5E10, pp. 1–28 (1945)

    Google Scholar 

  8. M. Drees, A theory of airflow through rotors and its application to some helicopter problems. J. Helicopter Assoc. Great Br. 3(2), 79–104 (1949)

    Google Scholar 

  9. A. Egolf, A.J. Landgrebe, Helicopter rotor wake geometry and its influence in forward flight. Technical report, NASA CR-3726 (1983)

    Google Scholar 

  10. S. Guntur, N. Troldborg, M. Gaunaa, Application of engineering models to predict wake deflection due to a tilted wind turbine, in EWEC (Copenhagen, 2012)

    Google Scholar 

  11. W. Haans, Wind turbine aerodynamics in yaw - unravelling the measured rotor wake. Ph.D. thesis, DU Wind - Delft University of Technology, 2011

    Google Scholar 

  12. H. Heyson, S. Katzoff, Normal component of induced velocity field in the vicinity of a lifting rotor with a nonuniform disk loading. Technical report, NACA TN-3690, Langley Aeronautical Laboratory, Langley Field (1956)

    Google Scholar 

  13. H. Heyson, S. Katzoff, Induced velocities near a lifting rotor with nonuniform disk loading. Technical report, NACA report 1319 (1957)

    Google Scholar 

  14. Á. Jiménez, A. Crespo, E. Migoya, Application of a LES technique to characterize the wake deflection of a wind turbine in yaw. Wind Energy 13(6), 559–572 (2010)

    Article  Google Scholar 

  15. W. Johnson, Helicopter Theory, 2nd edn., Dover Books on Physics (Dover Publications, Mineola, 1994)

    Google Scholar 

  16. J.G. Leishman, Principles of Helicopter Aerodynamics, vol. 12, 2nd edn., Cambridge Aerospace Series (Cambridge University Press, Cambridge, 2006)

    Google Scholar 

  17. K.W. Mangler, H.B. Squire, The induced velocity field of a rotor. Technical report, Aeronautical Research Council - R.&M. No. 2642 (1950)

    Google Scholar 

  18. M.K. McWilliam, S. Lawton, S.Cline, C. Crawford, A corrected blade element momentum method for simulating wind turbines in yawed flow, in Proceedings of 49th AIAA Meeting (Orlando, 2011), pp. 1–10

    Google Scholar 

  19. S. Øye, Induced velocities for rotors in yaw - an extension of the blade element momentum method, in Sixth IEA Symposium on the Aerodynamics of Wind Turbines, ECN, Petten (1992), pp. 1–5

    Google Scholar 

  20. D.M. Pitt, DAl Peters, Theoretical prediction of dynamic-inflow derivatives. Vertica 5, 21–34 (1981)

    Google Scholar 

  21. T. Sant, Improving BEM-based aerodynamics models in Wind turbine design codes. Ph.D. thesis, DU Wind - Delft University of Technology, 2007

    Google Scholar 

  22. J.G. Schepers, An Engineering Model for Yawed Conditions, Developed on the Basis of Wind Tunnel Measurements. ECN-RX-98-057. Netherlands Energy Research Foundation ECN, Petten (1998)

    Google Scholar 

  23. H. Snel and J.G. Schepers, Joint investigation of dynamic inflow effects and implementation of an engineering method. Technical report, ECN-C–94-107, Energy Research Centre of the Netherlands, Petten (1995)

    Google Scholar 

  24. N. Troldborg, M. Gaunaa, S. Guntur, Modelling the influence of yaw using a simple vortex rotor model, in EWEC (Copenhagen, 2012), pp. 1–5

    Google Scholar 

  25. G.J.W. Van Bussel, The use of the asymptotic acceleration potential method for horizontal axis windturbine rotor aerodynamics. J. Wind Eng. Ind. Aerodyn. 39, 161–172 (1992)

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Wind Energy, Aeroelastic Design, Technical University of Denmark, Roskilde, Denmark

    Emmanuel Branlard

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  1. Emmanuel Branlard
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Correspondence to Emmanuel Branlard .

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Branlard, E. (2017). Yaw-Modelling Using a Skewed Vortex Cylinder. In: Wind Turbine Aerodynamics and Vorticity-Based Methods. Research Topics in Wind Energy, vol 7. Springer, Cham. https://doi.org/10.1007/978-3-319-55164-7_21

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  • DOI: https://doi.org/10.1007/978-3-319-55164-7_21

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-55163-0

  • Online ISBN: 978-3-319-55164-7

  • eBook Packages: EnergyEnergy (R0)

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