Preprints
https://doi.org/10.5194/wes-2020-92
https://doi.org/10.5194/wes-2020-92
06 Jul 2020
 | 06 Jul 2020
Status: this preprint was under review for the journal WES but the revision was not accepted.

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

Moritz Mauz, Bram van Kesteren, Andreas Platis, Stefan Emeis, and Jens Bange

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, Bram van Kesteren, Andreas Platis, Stefan Emeis, and Jens Bange
 
Status: closed
Status: closed
AC: Author comment | RC: Referee comment | SC: Short comment | EC: Editor comment
Printer-friendly Version - Printer-friendly version Supplement - Supplement
 
Status: closed
Status: closed
AC: Author comment | RC: Referee comment | SC: Short comment | EC: Editor comment
Printer-friendly Version - Printer-friendly version Supplement - Supplement
Moritz Mauz, Bram van Kesteren, Andreas Platis, Stefan Emeis, and Jens Bange
Moritz Mauz, Bram van Kesteren, Andreas Platis, Stefan Emeis, and Jens Bange

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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.
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