Skip to main content

Detailed Analysis of the Joukowsky Model

  • Chapter
  • First Online:
General Momentum Theory for Horizontal Axis Wind Turbines

Part of the book series: Research Topics in Wind Energy ((RTWE,volume 4))

  • 2719 Accesses

Abstract

Due to the anomalous behaviour of the Joukowsky rotor, this model is analysed in details for small tip speed ratios. The analysis is carried analytically and by comparison to additional CFD computations and some recent experiments. It is found that the model only attains a well-defined optimum for tip speed ratios larger than 0.93, but that other inherent features of the equations by themselves will limit the power performance at smaller tip speed ratios.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  • Delery, J.M.: Aspects of vortex breakdown. Prog. Aerospace Sci. 30, 1–59 (1994)

    Article  Google Scholar 

  • De Vries, O.: Fluid dynamic aspects of wind energy conversion. AGARDograph No. 243. AGARD (1979). ISBN: 92-835-1326-6

    Google Scholar 

  • Glauert, H.: Airplane Propellers. In: Durand, W.F. (ed.) Division L in Aerodynamic Theory, vol. IV, pp. 169–360. Springer: Berlin (1935)

    Google Scholar 

  • Joukowsky, N.E.: Vortex theory of a rowing screw. Trudy Otdeleniya Fizicheskikh Nauk Obshchestva Lubitelei Estestvoznaniya 16, 1 (1912). (in Russian)

    MATH  Google Scholar 

  • Lam, G.C.K.: Wind energy conversion efficiency limit. Wind Eng. 30(5), 431 (2006)

    Article  Google Scholar 

  • Leweke, T., Quaranta, H.U., Mikkelsen, R.F., Sørensen, J.N.: Vortex breakdown and wake characteristics of a Joukowsky rotor at small tip speed ratios. In: Submitted to the Wake Conference, Visby, Sweden (2015)

    Google Scholar 

  • Madsen, H.A., Mikkelsen, R., Øye, S., Bak, B., Johansen, J.: A detailed investigation of the blade element momentum (BEM) model based on analytical and numerical results and proposal for modifications of the BEM model. Making torque from wind. J. Phys. Conf. Ser. 75, 012016 (2007). doi:10.1088/1742-6596/75/1/012016

    Article  Google Scholar 

  • Mikkelsen, R.F.: Actuator disc methods applied to wind turbines. Ph.D. Dissertation, Technical University of Denmark, MEK-FM-PHD 2003-02 (2003)

    Google Scholar 

  • Mikkelsen, R.F., Øye, S., Sørensen, J.N., Madsen, H.Aa., Shen, W.Z.: Analysis of wake expansion and induction near tip. In: Proceedings of EWEC 2009, European Wind Energy Association (EWEA), Brussels (2009)

    Google Scholar 

  • Sharpe, D.J.: A general momentum theory applied to an energy-extracting actuator disc. Wind Energy 7, 177–188 (2004)

    Article  Google Scholar 

  • Sørensen, J.N., Kock, C.W.: A model for unsteady rotor aerodynamics. J. Wind Eng. Ind. Aerodyn. 58, 259–275 (1995)

    Google Scholar 

  • Sørensen, J.N., Mikkelsen, R.: An upper limit of the power performance of wind turbines operating at low tip speed ratios (2015). (To be submitted)

    Google Scholar 

  • Sørensen, J.N., Myken, A.: Unsteady actuator disc model for horizontal axis wind turbines. J. Wind Eng. Ind. Aerodyn. 139, 139–149 (1992)

    Article  Google Scholar 

  • Sørensen, J.N., Shen, W.Z., Munduate, X.: Analysis of wake-states by a full-field actuator disc model. Wind Energy 1, 73–88 (1998)

    Article  Google Scholar 

  • Sørensen, J.N., van Kuik, G.A.M.: General momentum theory for wind turbines at low tip speed ratios. Wind Energy 14, 821–839 (2011)

    Article  Google Scholar 

  • Squire, H.B.: Analysis of the vortex breakdown phenomenon, Part I. Imperial College of Science and Technology, Report no. 102 (1960)

    Google Scholar 

  • Wilson, R.E., Lissaman, P.B.S.: Applied aerodynamics of wind power machines. Oregon State University, Corvallis (1974)

    Google Scholar 

  • Wood, D.H.: Including swirl in the actuator disc analysis of wind turbines. Wind Eng. 31(5), 317–323 (2007)

    Article  Google Scholar 

  • Xiros, M.I., Xiros, N.I.: 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, 99–102 (2007)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Jens Nørkær Sørensen .

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Sørensen, J.N. (2016). Detailed Analysis of the Joukowsky Model. In: General Momentum Theory for Horizontal Axis Wind Turbines. Research Topics in Wind Energy, vol 4. Springer, Cham. https://doi.org/10.1007/978-3-319-22114-4_6

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-22114-4_6

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-22113-7

  • Online ISBN: 978-3-319-22114-4

  • eBook Packages: EnergyEnergy (R0)

Publish with us

Policies and ethics