Hostname: page-component-848d4c4894-2pzkn Total loading time: 0 Render date: 2024-05-03T06:34:20.868Z Has data issue: false hasContentIssue false
  • English
  • Français

A simplified vortex model of propeller and wind-turbine wakes

Published online by Cambridge University Press:  14 May 2013

Antonio Segalini  and
P. Henrik Alfredsson
Antonio Segalini*
Affiliation:
Linné FLOW Centre, KTH Mechanics, S-100 44 Stockholm, Sweden
P. Henrik Alfredsson
Affiliation:
Linné FLOW Centre, KTH Mechanics, S-100 44 Stockholm, Sweden
*
†Email address for correspondence: segalini@mech.kth.se
Get access Rights & Permissions [Opens in a new window]

Abstract

A new vortex model of inviscid propeller and wind-turbine wakes is proposed based on an asymptotic expansion of the Biot–Savart induction law to account for the finite vortex core size. The circulation along the blade is assumed to be constant from the blade root to the tip approximating a turbine with maximum power production for given operating conditions. The model iteratively calculates the tip-vortex path, allowing the wake to expand/contract freely, and is afterward able to evaluate the velocity field in the whole domain. The ‘roller-bearing analogy’, proposed by Okulov and Sørensen (J. Fluid Mech., vol. 649, 2010, pp. 497–508), is used to determine the vortex core size. A comparison of the main outcomes of the present model with the general momentum theory is performed in terms of the operating parameters (namely the number of blades, the tip-speed ratio, the blade circulation and the vortex core size), demonstrating good agreement between the two. Furthermore, experimental data have been compared with the model outputs to validate the model under real operating conditions.

JFM classification

Vortex Flows: Vortex Flows Vortex Flows: Vortex dynamics Wakes/Jets: Wakes/Jets
Type
Papers
Information
Journal of Fluid Mechanics , Volume 725 , 25 June 2013 , pp. 91 - 116
Copyright
©2013 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Abramowitz, M. & Stegun, I. A. 1972 Handbook of Mathematical Functions. US National Bureau of Standards.Google Scholar
Batchelor, G. K. 2000 An Introduction to Fluid Dynamics, p. 615. Cambridge University Press.CrossRefGoogle Scholar
Bhagwat, M. J. & Leishman, J. G. 2000 On the aerodynamic stability of helicopter rotor wakes. American Helicopter Society 56th Annual Forum, Virginia Beach, VA, May 24, 2000.Google Scholar
Boersma, J. & Wood, D. H. 1999 On the self-induced motion of a helical vortex. J. Fluid Mech. 384, 263–280.Google Scholar
Burton, T., Sharpe, D., Jenkins, N. & Bossanyi, E. 2001 Wind Energy Handbook, p. 617. John Wiley & Sons.Google Scholar
Callegari, A. J. & Ting, L. 1978 Motion of a curved vortex filament with decaying vortical core and axial velocity. J. Appl. Maths 35, 148–175.Google Scholar
Chattot, J.-J. 2002 Design and analysis of wind turbines using helicoidal vortex model. Comput. Fluid Dyn. J. 11, 50–54.Google Scholar
Conway, J. T. 1998 Exact actuator disk solutions for non-uniform heavy loading and slipstream contraction. J. Fluid Mech. 365, 235–267.Google Scholar
Favier, D., Ettaouil, A. & Maresca, C. 1989 Numerical and experimental investigation of isolated propeller wakes in axial flight. J. Aircraft 26, 837–846.CrossRefGoogle Scholar
Felli, M., Camussi, R. & Felice, F. Di 2011 Mechanisms of evolution of the propeller wake in the transition and far fields. J. Fluid Mech. 682, 5–53.Google Scholar
Fukumoto, Y. & Miyazaki, T. 1991 Three-dimensional distortions of a vortex filament with axial velocity. J. Fluid Mech. 222, 369–416.CrossRefGoogle Scholar
Glauert, H. 1935 Airplane propellers. In Division L in Aerodynamic Theory (ed. Durand, W. F.), vol. 4, pp. 169–360. Springer.CrossRefGoogle Scholar
Goldstein, S. 1929 On the vortex theory of screw propellers. Proc. R. Soc. Lond. A 123, 440–465.Google Scholar
Hama, F. R. 1962 Progressive deformation of a curved vortex filament by its own induction. Phys. Fluids 5, 1156–1162.Google Scholar
Hasimoto, H. 1972 A soliton on a vortex filament. J. Fluid Mech. 51, 477–485.Google Scholar
Joukowsky, N. E. 1912 Vortex theory of screw propeller. I. Trudy Otdeleniya Fizicheskikh Nauk Obshchestva Lubitelei Estestvoznaniya 16 (1), 1–31 (in Russian). French translation in: Théorie tourbillonnaire de l’hélice propulsive (Gauthier–Villars, Paris, 1929) 1–47.Google Scholar
Katz, J. & Plotkin, A. 2001 Low-Speed Aerodynamics, p. 630. Cambridge University Press.Google Scholar
Kuibin, P. A. & Okulov, V. L. 1998 Self-induced motion and asymptotic expansion of the velocity field in the vicinity of a helical vortex filament. Phys. Fluids 10, 607–614.CrossRefGoogle Scholar
Leishman, J. G. 2000 Principles of Helicopter Aerodynamics, p. 496. Cambridge University Press.Google Scholar
Medici, D. & Alfredsson, P. H. 2006 Measurements on a wind turbine wake: 3D effects and bluff body vortex shedding. Wind Energy 9, 219–236.Google Scholar
Medici, D., Ivanell, S., Dahlberg, J.-Å. & Alfredsson, P. H. 2011 The upstream flow of a wind turbine: blockage effect. Wind Energy 14, 691–697.Google Scholar
Mikkelsen, R. 2003 Actuator disc methods applied to wind turbines. PhD thesis, Department of Mechanical Engineering, Technical University of Denmark.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. 2010 Maximum efficiency of wind turbine rotors using joukowsky and betz approaches. J. Fluid Mech. 649, 497–508.CrossRefGoogle Scholar
Okulov, V. L. & van Kuik, G. A. M. 2012 The Betz–Joukowsky limit: on the contribution to rotor aerodynamics by the British, German and Russian scientific schools. Wind Energy 15, 335–344.Google Scholar
Pistolesi, E. 1932 Aerodinamica. Unione tipografico-editrice torinese.Google Scholar
Ricca, R. L. 1994 The effect of torsion on the motion of a helical vortex filament. J. Fluid Mech. 273, 241–259.CrossRefGoogle Scholar
Saffman, P. G. 1992 Vortex Dynamics, p. 311. Cambridge University Press.Google Scholar
Schepers, G., Pascal, L. & Snel, H. 2010 First results from Mexnext: analysis of detailed aerodynamic measurements on a 4.5 m diameter rotor placed in the large German Dutch Wind Tunnel DNW. In European Wind Energy Conference and Exhibition (EWEC), April 20–23, 2010, Warsaw, Poland.Google Scholar
Shen, W. Z., Mikkelsen, R. & Sørensen, J. N. 2005 Tip loss corrections for wind turbine computations. Wind Energy 8, 457–475.Google Scholar
Sørensen, J. N. & Shen, W. Z. 2002 Numerical modelling of wind turbine wakes. Trans. ASME: J. Fluids Engng 124, 393–399.Google Scholar
Spalart, P. 2003 On the simple actuator disk. J. Fluid Mech. 494, 399–405.Google Scholar
Troldborg, N. 2008 Actuator line modelling of wind turbine wakes. PhD thesis, Technical University of Denmark.Google Scholar
Valiron, G. 1986 The Classical Differential Geometry of Curves and Surfaces, p. 286. Math Sci Press.Google Scholar
Vermeer, L. J., Sørensen, J. N. & Crespo, A. 2003 Wind turbine wake aerodynamics. Prog. Aerosp. Sci. 39, 467–510.CrossRefGoogle Scholar
Voutsinas, S. G. 2006 Vortex methods in aeronautics: how to make things work. Intl J. Comput. Fluid Dyn. 20 (1), 3–18.CrossRefGoogle Scholar
Wood, D. H. & Boersma, J. 2001 On the motion of multiple helical vortices. J. Fluid Mech. 447, 149–171.Google Scholar