Abstract
The turbulence time and length scales of a single wind turbine wake subjected to atmospheric turbulence are calculated from two large eddy simulations that differ in ambient turbulence intensity. The smallest turbulence length scale in the wake is about half the rotor radius and it increases for higher ambient turbulence levels. The large eddy simulations are compared with Reynolds-averaged Navier-Stokes simulations employing the standard and three extended k-ε models: the k-ε-fP model of van der Laan, the k-ε model of Shih and k-ε model of Durbin. It is shown that all three extended k-ε models can be written in a similar form. All Reynolds-averaged Navier-Stokes based turbulence models predict turbulence time scales that are comparable to the turbulence time scales of the large eddy simulations. The standard k-ε model underpredicts the velocity deficit because the turbulence length scale is overpredicted compared to the large eddy simulations. The performance of the k-ε model of Durbin shows to be very dependent on the ambient turbulence level and it is therefore less suited for wind turbine wake simulations. The k-ε model of Shih and the k-ε-fP model of van der Laan are recommended to be used for wind turbine wake simulations because their results are similar and compare well with results of large eddy simulations for both a low and high ambient turbulence intensity due to a limitation of the turbulence length scale in the near wake.
Highlights
Wind turbine wakes can cause energy losses and increase wind turbine loads in wind farms
The turbulence time and length scales of a single wind turbine wake operating in atmospheric turbulence are calculated from two Large eddy simulation (LES) that differ in ambient turbulence intensity
Two methods are used to calculate the turbulence scales: a method based on fitting an exponential function with the autocorrelation to obtain a turbulence time scale and a method based on fitting a Kaimal spectrum to extract a turbulence length scale
Summary
Wind turbine wakes can cause energy losses and increase wind turbine loads in wind farms. A number of RANS modelers [3, 4, 5, 6, 7] including ourselves, have developed new and applied existing extended k-ε models to overcome this issue Most of these models limit the eddy viscosity in the wake by reducing the turbulence length and/or time scales. The extended k-ε models can show an improvement of the velocity deficit and turbulence intensity in the wake but not much is known about how well the limited turbulence length and time scales compare with those of LES. We use LES data of two single wind turbine wake cases operating in atmospheric turbulence to investigate if the turbulence length and time scales from LES compare well with the turbulence length and time scales calculated by RANS using the standard and three extended k-ε models. Since the wall boundary in the LESs is a slip wall and the inserted Mann turbulence is not connected to the wall boundary, the turbulence scales do not vary much with height, which allows the use of ring-averaging
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