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Wind Energy Science The interactive open-access journal of the European Academy of Wind Energy
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https://doi.org/10.5194/wes-2020-92
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/wes-2020-92
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.

  06 Jul 2020

06 Jul 2020

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This preprint is currently under review for the journal WES.

An analytical solution for wind deficit decay behind a wind energy converter using momentum flux conservation validated by UAS data

Moritz Mauz1, Bram van Kesteren1, Andreas Platis1, Stefan Emeis2, and Jens Bange1 Moritz Mauz et al.
  • 1Centre for Applied Geoscience, University of Tübingen, 72074 Tübingen, Germany
  • 2Institute for Meteorology and Climate Research, Karlsruhe Institute of Technology, 82467 Garmisch-Partenkirchen, Germany

Abstract. The wind deficit behind a wind energy converter (WEC) results from a complex interaction of forces. Kinetic energy is removed from the atmosphere, but coherent turbulent structures prevent a swift compensation of momentum within the wake behind the WEC. A detailed description of the wake is beneficial in meso-scale weather forecast (e.g. WRF models) and numerical simulations of wind wake deficits. Especially in the near to intermediate wake (0.5–5 rotor diameter D), the dominating processes characterising the wake formation change along the wake. The conservation equation of momentum is used as a starting point to map the most important processes assuming the WEC operates at maximum efficiency in a neutral stratified boundary layer. The wake is divided into three different regions to accommodate the changing impact of atmospheric turbulence and the shear created by the WEC onto the wake. A differential equation that depicts the variable momentum transport into the wind deficit along the wake is derived and solved analytically. Additionally, a numerical solution (Euler method) of the simplified momentum conservation equation is shown to provide a quality control and error estimate to the analytical model. The analytical solution is compared to in-situ wake measurements behind an Enercon E-112 converter, located in the Jade Wind Park near the North Sea coast in Germany, captured by the MASC-3 UAS (unmanned aircraft system) of the University of Tübingen. The obtained UAS data cover the distance from 0.5–5 D at hub height behind the nacelle. The analytical and numerical model are found to be in good agreement with the data of the three measurement flights behind the WEC.

Moritz Mauz et al.

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Moritz Mauz et al.

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Short summary
The submitted manuscript suggests an analytical model/approach to connect the near-wake wind deficit with the mid an far-wake deficit. The atmospheric turbulence is considered as the main driver for the wind deficit decay rate in this approach. The analytical solution is backed by a numerical solution of the momentum conservation equation derived from Navier-Stokes equations. In-situ wake UAS measurements are the basis and motivation for the model approach shown in the manuscript.
The submitted manuscript suggests an analytical model/approach to connect the near-wake wind...
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