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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    Abstract

    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)
    Volume524
    Issue number1
    Number of pages1
    ISSN1742-6596
    DOIs
    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
    http://indico.conferences.dtu.dk/conferenceDisplay.py?confId=138

    Conference

    Conference5th International Conference on The Science of Making Torque from Wind 2014
    Number5
    LocationTechnical University of Denmark
    Country/TerritoryDenmark
    CityCopenhagen
    Period10/06/201420/06/2014
    Internet address

    Bibliographical note

    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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