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Research Papers

Implementation of a Mixing Length Turbulence Formulation Into the Dynamic Wake Meandering Model

[+] Author and Article Information
Rolf-Erik Keck1

Rotor Systems,Vestas Wind Systems A/S, DK-4000 Roskilde, Denmark; Wind Energy Department, Risø DTU National Laboratory for Sustainable Energy, DK-4000 Roskilde, Denmarkroeke@vestas.com

Dick Veldkamp

Rotor Systems,Vestas Wind Systems A/S, DK-4000 Roskilde, Denmark

Helge Aagaard Madsen, Gunner Larsen

Wind Energy Department,Risø DTU National Laboratory for Sustainable Energy, DK-4000 Roskilde, Denmark

1

Corresponding author.

J. Sol. Energy Eng 134(2), 021012 (Mar 19, 2012) (13 pages) doi:10.1115/1.4006038 History: Received May 30, 2011; Revised February 06, 2012; Published March 15, 2012; Online March 19, 2012

The work presented in this paper focuses on improving the description of wake evolution due to turbulent mixing in the dynamic wake meandering (DWM) model. From wake investigations performed with high-fidelity actuator line simulations carried out in ELLIPSYS3D , it is seen that the current DWM description, where the eddy viscosity is assumed to be constant in each cross-section of the wake, is insufficient. Instead, a two-dimensional eddy viscosity formulation is proposed to model the shear layer generated turbulence in the wake, based on the classical mixing length model. The performance of the modified DWM model is verified by comparing the mean wake velocity distribution with a set of ELLIPSYS3D actuator line calculations. The standard error (defined as the standard deviation of the difference between the mean velocity field of the DWM and the actuator line model), in the wake region extending from 3 to 12 diameters behind the rotor, is reduced by 27% by using the new eddy viscosity formulation.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 1

A high level calculation sequence of the DWM model including required input and delivered output

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Figure 2

Sketch of the computational domain. The left figure is an X–Y plane showing the cross-section of the domain, and the right figure is an X–Z plane showing the domain from above. The outer solid box represents the computational domain. The rotor location is indicated by the solid black body. The dashed line/box indicates where the turbulent fluctuations are applied, and the solid box shows the refined region.

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Figure 3

The development of axial velocity in four different actuator line resolutions: 14, 25, 38, and 51 points per radii (p per R). The left figure is at the rotor plane, the middle figure is at 1D, and the right figure is at 3D downstream of the turbine. The 51 p per R case is missing at 3D as the computational domain used was too short to extract data so far downstream.

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Figure 4

The development of wake turbulence intensity in four different actuator line resolutions: 14, 25, 38, and 51 points per radii (p per R). The left figure is at the rotor plane, the middle figure is at 1D, and the right figure is at 3D downstream of the turbine. The 51 p per R case is missing at 3D as the computational domain used was too short to extract data so far downstream.

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Figure 5

The development of turbulent energy spectra in four different grid resolutions in the wake region: 14, 25, 38, and 51 points per radii (p per R). The figure shows the energy spectra in streamwise, vertical, and horizontal directions (left, middle, and right figure, respectively).

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Figure 6

The development of turbulent energy spectra in two sizes of the wake refined region in the actuator line resolutions: 4 × 4 and 6 × 6 radius. The figure shows the energy spectra in streamwise, vertical, and horizontal direction (left, middle, and right figure, respectively).

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Figure 7

The development of axisymmetric eddy viscosity from a set of actuator line simulations of an NM80 Turbine. The eddy viscosity is extracted from the turbulent kinetic energy balance (“k”) in the simulations based on two different models, the Johnson–King model (left column, Eq. 7) and the standard eddy viscosity model (right column, Eq. 11). Radial eddy viscosity profiles are extracted 1, 3, 6, 9, 12, and 15D downstream of the rotor, and inflow conditions are wind speed of 10 m/s and ambient turbulence intensity of 0%, 6%, and 14% (top, middle, and bottom row).

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Figure 8

Comparisons of the mean streamwise velocity distribution between the calibrated standard DWM model (left) and the mixing length DWM model (right) to actuator line data. The mixing length DWM model captures the velocity distribution in the wake better than the standard DWM model. The improvements are especially clear at 3D, where the shape of the wake deficit is improved.

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Figure 9

The result of calibration by least-square fit to actuator line data for the DWM model with the mixing length eddy viscosity by using the iterative calibration method. Overall, a very good agreement is seen for all four cases presented.

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