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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: [email protected]
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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 

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