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Applications of 2D helical vortex dynamics

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Abstract

In the paper, we show how the assumption of helical symmetry in the context of 2D helical vortices can be exploited to analyse and to model various cases of rotating flows. From theory, examples of three basic applications of 2D dynamics of helical vortices embedded in flows with helical symmetry of the vorticity field are addressed. These included some of the problems related to vortex breakdown, instability of far wakes behind rotors and vortex theory of ideal rotors.

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References

  1. Dritschel D.G.: Generalized helical Beltrami flows in hydrodynamics and magneto hydrodynamics. J. Fluid Mech. 222, 525–541 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  2. Okulov V.L.: Determination of the velocity field induced by vortex filaments of cylindric and weak conic shapes. Russ. J. Eng. Thermophys. 5(2), 63–75 (1995)

    MathSciNet  Google Scholar 

  3. Alekseenko S.V., Kuibin P.A., Okulov V.L., Shtork S.I.: Helical vortices in swirl flow. J. Fluid Mech. 382, 195–243 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  4. Troldborg, N.: Actuator Line Modelling of Wind Turbine Wakes. PhD thesis, Technical University of Denmark (2008)

  5. Velte C.M., Hansen M.O.L., Okulov V.L.: Helical structure of longitudinal vortices embedded in turbulent wall-bounded flow. J. Fluid Mech. 619, 167–177 (2009)

    Article  MATH  Google Scholar 

  6. Hardin J.C.: The velocity field induced by a helical vortex filament. Phys. Fluids 25, 1949–1952 (1982)

    Article  MATH  Google Scholar 

  7. Fukumoto, Y., Okulov, V.L.: The velocity field induced by a helical vortex tube. Phys. Fluids 17(10), 107101(1–19) (2005)

  8. Boersma J., Wood D.H.: On the self-induced motion of a helical vortex. J. Fluid Mech. 384, 263–280 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  9. Okulov V.L.: On the stability of multiple helical vortices. J. Fluid Mech. 521, 319–342 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  10. Goldstein S.: On the vortex theory of screw propellers. Proc. R. Soc. Lond. A 123(792), 440–465 (1929)

    Article  Google Scholar 

  11. Okulov V.L., Sørensen J.N.: Stability of helical tip vortices in a rotor far wake. J. Fluid Mech. 576, 1–25 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  12. Hall M.G.: Vortex breakdown. Annu. Rev. Fluid Mech. 4, 195–218 (1972)

    Article  Google Scholar 

  13. Leibovich S.: The structure of vortex breakdown. Annu. Rev. Fluid Mech. 10, 221–246 (1978)

    Article  Google Scholar 

  14. Lucca-Negro O., O’Doherty T.: Vortex breakdown: a review. Prog. Energy Combust. Sci. 27(4), 431–481 (2001)

    Article  Google Scholar 

  15. Garg A.K., Leibovich S.: Spectral characteristics of vortex breakdown flow fields. Phys. Fluids 22, 2053–2964 (1979)

    Article  Google Scholar 

  16. Okulov V.L.: The transition from the right helical symmetry to the left symmetry during vortex breakdown. Tech. Phys. Lett. 22(10), 798–800 (1996)

    Google Scholar 

  17. Murakhtina T., Okulov V.: Changes in topology and symmetry of vorticity field during the turbulent vortex breakdown. Tech. Phys. Lett. 26(10), 432–435 (2000)

    Article  Google Scholar 

  18. Okulov V.L., Sørensen J.N., Voigt L.K.: Vortex scenario and bubble generation in a cylindrical cavity with rotating top and bottom. Eur. J. Mech. B 24(1), 137–148 (2005)

    Article  MATH  Google Scholar 

  19. Joukowski N.E.: Vortex theory of a propeller screw. Trudy Otdeleniya Fizicheskikh Nauk Obshchestva Lyubitelei Estestvoznaniya 16, 1 (1912) (in Russian)

    Google Scholar 

  20. Gupta B.P., Loewy R.G.: Theoretical analysis of the aerodynamic stability of multiple, interdigitated helical vortices. AIAA J. 12(10), 1381–1387 (1974)

    Article  MATH  Google Scholar 

  21. Widnall S.E.: The stability of a helical vortex filament. J. Fluid Mech. 54, 641–663 (1972)

    Article  MATH  Google Scholar 

  22. Bhagwat M.J., Leishman J.G.: Stability analysis of helicopter rotor wakes in axial flight. J. Am. Helicopter Ass. 45, 165–178 (2000)

    Article  Google Scholar 

  23. Vermeer L.J., Sorensen J.N., Crespo A.: Wind Turbine Wake Aerodynamics. Prog. Aerosp. Sci. 39, 467–510 (2003)

    Article  Google Scholar 

  24. Felli M., Guj G., Camussi R.: Effect of the number of blades on propeller wake evolution. Exp. Fluids 44, 409–418 (2008)

    Article  Google Scholar 

  25. Betz A.: Das Maximum der theoretisch möglichen Ausnützung des Windes durch Windmotoren. Zeitschrift für das gesamte Turbinenwesen 26, 307–309 (1920)

    Google Scholar 

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

    Google Scholar 

  27. Chattot J.-J.: Optimization of wind turbines using helicoidal vortex model. Trans. ASME 125, 418–424 (2003)

    Google Scholar 

  28. Wood D.H., Boersma J.: On the motion of multiple helical vortices. J. Fluid Mech. 447, 149–171 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  29. Betz, A.: Schraubenpropeller mit Geringstem Energieverlust, Dissertation, Gottingen Nachrichten, Gottingen, (1919)

  30. Theodorsen T.: Theory of propellers. McGraw-Hill, New York (1948)

    Google Scholar 

  31. Wald Q.R.: The aerodynamics of propellers. Prog. Aerosp. Sci. 42, 85–128 (2006)

    Article  Google Scholar 

  32. Okulov V.L., Sørensen J.N.: Refined Betz limit for rotors with a finite number of blades. Wind energy 11, 415–426 (2008)

    Article  Google Scholar 

Download references

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Authors and Affiliations

  1. Department of Mechanical Engineering and Center for Fluid Dynamics, Technical University of Denmark, 2800, Lyngby, Denmark

    Valery L. Okulov & Jens N. Sørensen

Authors
  1. Valery L. Okulov
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  2. Jens N. Sørensen
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Correspondence to Valery L. Okulov.

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Communicated by H. Aref

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Okulov, V.L., Sørensen, J.N. Applications of 2D helical vortex dynamics. Theor. Comput. Fluid Dyn. 24, 395–401 (2010). https://doi.org/10.1007/s00162-009-0136-3

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  • DOI: https://doi.org/10.1007/s00162-009-0136-3

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