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Research Papers

# Analysis and Modifications of Turbulence Models for Wind Turbine Wake Simulations in Atmospheric Boundary Layers

[+] Author and Article Information
Enrico G. A. Antonini

Department of Mechanical
and Industrial Engineering,
University of Toronto,
e-mail: enrico.antonini@mail.utoronto.ca

David A. Romero

Department of Mechanical
and Industrial Engineering,
University of Toronto,
e-mail: d.romero@utoronto.ca

Cristina H. Amon

Professor
Department of Mechanical
and Industrial Engineering,
University of Toronto,
e-mail: cristina.amon@utoronto.ca

Contributed by the Solar Energy Division of ASME for publication in the JOURNAL OF SOLAR ENERGY ENGINEERING: INCLUDING WIND ENERGY AND BUILDING ENERGY CONSERVATION. Manuscript received January 9, 2017; final manuscript received February 13, 2018; published online March 13, 2018. Assoc. Editor: Douglas Cairns.

J. Sol. Energy Eng 140(3), 031007 (Mar 13, 2018) (13 pages) Paper No: SOL-17-1013; doi: 10.1115/1.4039377 History: Received January 09, 2017; Revised February 13, 2018

## Abstract

Computational fluid dynamics (CFD) simulations of wind turbine wakes are strongly influenced by the choice of the turbulence model used to close the Reynolds-averaged Navier-Stokes (RANS) equations. A wrong choice can lead to incorrect predictions of the velocity field characterizing the wind turbine wake and, consequently, to an incorrect power estimation for wind turbines operating downstream. This study aims to investigate the influence of different turbulence models, namely the $k–ε, k–ω, SSTk–ω$, and Reynolds stress models (RSM), on the results of CFD wind turbine simulations. Their influence was evaluated by comparing the CFD results with the publicly available experimental measurements of the velocity field and turbulence quantities from the Sexbierum and Nibe wind farms. Consistent turbulence model constants were proposed for atmospheric boundary layer (ABL) and wake flows according to previous literature and appropriate experimental observations, and modifications of the derived turbulence model constants were also investigated in order to improve agreement with experimental data. The results showed that the simulations using the k–ε and k–ω turbulence models consistently overestimated the velocity and turbulence quantities in the wind turbine wakes, whereas the simulations using the shear-stress transport (SST) k–ω and RSMs could accurately match the experimental data. Results also showed that the predictions from the k–ε and k–ω turbulence models could be improved by using the modified set of turbulence coefficients.

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## Figures

Fig. 2

Schematic layouts of the domain: (a) top view, (b) lateral view, and (c) front view

Fig. 1

Performance curves of the Sexbierum and Nibe wind turbines: (a) Sexbierum wind turbine and (b) Nibe wind turbine

Fig. 7

Wind speed and TI downstream the Nibe wind turbine as a function of wind direction for the kϵ model with the baseline and modified sets of coefficients: (a) 2.5D downstream, (b) 4D downstream, (c) 7.5D downstream, (d) 2.5D downstream, (e) 4D downstream, and (f) 7.5D downstream

Fig. 8

Wind speed and TI downstream the Nibe wind turbine as a function of wind direction for the kω model with the baseline and modified sets of coefficients: (a) 2.5D downstream, (b) 4D downstream (c) 7.5D downstream, (d) 2.5D downstream, (e) 4D downstream, and (f) 7.5D downstream

Fig. 9

Wind speed and TI downstream the Nibe wind turbine as a function of wind direction for the SST kω model with the baseline and modified sets of coefficients: (a) 2.5D downstream, (b) 4D downstream, (c) 7.5D downstream, (d) 2.5D downstream, (e) 4D downstream, and (f) 7.5D downstream

Fig. 10

Wind speed and TI downstream the Nibe wind turbine as a function of wind direction for the RSM with the baseline and modified sets of coefficients: (a) 2.5D downstream, (b) 4D downstream, (c) 7.5D downstream, (d) 2.5D downstream, (e) 4D downstream, and (f) 7.5D downstream

Fig. 3

Wind speed and turbulence kinetic energy downstream the Sexbierum wind turbine as a function of wind direction for the kϵ model with the baseline and modified sets of coefficients: (a) 2.5D downstream, (b) 5.5D downstream, (c) 8D downstream, (d) 2.5D downstream, (e) 5.5D downstream, and (f) 8D downstream

Fig. 4

Wind speed and turbulence kinetic energy downstream the Sexbierum wind turbine as a function of wind direction for the kω model with the baseline and modified sets of coefficients: (a) 2.5D downstream, (b) 5.5D downstream, (c) 8D downstream, (d) 2.5D downstream, (e) 5.5D downstream, and (f) 8D downstream

Fig. 5

Wind speed and turbulence kinetic energy downstream the Sexbierum wind turbine as a function of wind direction for the SST kω model with the baseline and modified sets of coefficients: (a) 2.5D downstream, (b) 5.5D downstream, (c) 8D downstream, (d) 2.5D downstream, (e) 5.5D downstream, and (f) 8D downstream

Fig. 6

Wind speed and turbulence kinetic energy downstream the Sexbierum wind turbine as a function of wind direction for the RSM with the baseline and modified sets of coefficients: (a) 2.5D downstream, (b) 5.5D downstream, (c) 8D downstream, (d) 2.5D downstream, (e) 5.5D downstream, and (f) 8D downstream

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