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Self-similar behaviour of a rotor wake vortex core

Published online by Cambridge University Press:  08 January 2014

Mohamed Ali  and
Malek Abid
Mohamed Ali
Affiliation:
Institut de Recherche sur les Phénomènes Hors Équilibre (IRPHE), CNRS, UMR 7342, Centrale Marseille, and Aix-Marseille Université, 49, rue F. Joliot Curie, B.P. 146, 13384 Marseille CEDEX 13, France
Malek Abid*
Affiliation:
Institut de Recherche sur les Phénomènes Hors Équilibre (IRPHE), CNRS, UMR 7342, Centrale Marseille, and Aix-Marseille Université, 49, rue F. Joliot Curie, B.P. 146, 13384 Marseille CEDEX 13, France
*
†Email address for correspondence: [email protected]
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Abstract

We report a self-similar behaviour of solutions (obtained numerically) of the Navier–Stokes equations behind a single-blade rotor. That is, the helical vortex core in the wake of a rotating blade is self-similar as a function of its age. Profiles of vorticity and azimuthal velocity in the vortex core are characterized, their similarity variables are identified and scaling laws of these variables are given. Solutions of incompressible three-dimensional Navier–Stokes equations for Reynolds numbers up to $Re= 2000$ are considered.

JFM classification

Wakes/Jets: Wakes Vortex Flows: Vortex dynamics
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 740 , 10 February 2014 , R1
Copyright
©2014 Cambridge University Press 

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References

Abid, M. & Brachet, M. E. 1993 Numerical characterization of the dynamics of vortex filaments in round jets. Phys. Fluids A 5 (11), 2582–2584.Google Scholar
Abid, M. & Brachet, M. E. 1998 Direct numerical simulations of the Batchelor trailing vortex by a spectral method. Phys. Fluids 10 (2), 469–475.Google Scholar
Fukumoto, Y. & Okulov, V. L. 2005 The velocity field induced by a helical vortex tube. Phys. Fluids 17, 107101.Google Scholar
Hansen, M., Sørensen, J., Voutsinas, S., Sørensen, N. & Madsen, H. 2006 State of the art in wind turbine aerodynamics and aeroelasticity. Prog. Aerosp. Sci. 42, 285–330.CrossRefGoogle Scholar
Lucas, D. & Dritschel, D. G. 2009 A family of helically symmetric vortex equilibria. J. Fluid Mech. 634, 245–268.Google Scholar
Okulov, V. L. 2004 On the stability of multiple helical vortices. J. Fluid Mech. 521, 319–342.Google Scholar
Okulov, V. L. & Sørensen, J. N. 2007 Stability of helical tip vortices in a rotor far wake. J. Fluid Mech. 576, 1–25.Google Scholar
Poincaré, H. 1891 Théorie des Tourbillons, chap. 10. Jacques Gabay.Google Scholar
Saffman, P. G. 1992 Vortex Dynamics, p. 252. Cambridge University Press.Google Scholar
Sørensen, J. & Shen, W. Z. 2002 Numerical modelling of wind turbine wakes. J. Fluids Engng 124 (2), 393–399.Google Scholar
Thomson, T. L., Komerath, N. M. & Gray, R. B. 1988 Visualization and measurement of the tip vortex core of a rotor blade in hover. J. Aircraft 25, 1113–1121.CrossRefGoogle Scholar
Vermeer, L., Sørensen, J. & Crespo, A. 2003 Wind turbine wake aerodynamics. Prog. Aerosp. Sci. 39, 467–510.Google Scholar
Verzicco, R. & Orlandi, P. 1996 A finite-difference scheme for three-dimensional incompressible flows in cylindrical coordinates. J. Comput. Phys. 123 (2), 402–414.Google Scholar
Widnall, S. E. 1972 The stability of a helical vortex filament. J. Fluid Mech. 54 (4), 641–663.Google Scholar