Determination of Wind Turbine Near-Wake Length Based on Stability Analysis

Jens Nørkær Sørensen, Robert Flemming Mikkelsen, Sasan Sarmast, Stefan Ivanell, Dan Henningson

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A numerical study on the wake behind a wind turbine is carried out focusing on determining the length of the near-wake based on the instability onset of the trailing tip vortices shed from the turbine blades. The numerical model is based on large-eddy simulations (LES) of the Navier-Stokes equations using the actuator line (ACL) method. The wake is perturbed by applying stochastic or harmonic excitations in the neighborhood of the tips of the blades. The flow field is then analyzed to obtain the stability properties of the tip vortices in the wake of the wind turbine. As a main outcome of the study it is found that the amplification of specific waves (traveling structures) along the tip vortex spirals is responsible for triggering the instability leading to wake breakdown. The presence of unstable modes in the wake is related to the mutual inductance (vortex pairing) instability where there is an out-of-phase displacement of successive helix turns. Furthermore, using the non-dimensional growth rate, it is found that the pairing instability has a universal growth rate equal to π/2. Using this relationship, and the assumption that breakdown to turbulence occurs once a vortex has experienced sufficient growth, we provide an analytical relationship between the turbulence intensity and the stable wake length. The analysis leads to a simple expression for determining the length of the near wake. This expression shows that the near wake length is inversely proportional to thrust, tip speed ratio and the logarithmic of the turbulence intensity.
Original languageEnglish
Article number012155
Book seriesJournal of Physics: Conference Series (Online)
Issue number1
Number of pages1
Publication statusPublished - 2014
Event5th International Conference on The Science of Making Torque from Wind 2014 - Technical University of Denmark, Copenhagen, Denmark
Duration: 10 Jun 201420 Jun 2014
Conference number: 5


Conference5th International Conference on The Science of Making Torque from Wind 2014
LocationTechnical University of Denmark
Internet address

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Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Published under licence by IOP Publishing Ltd

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