A linearized numerical model of wind-farm flows

Abstract

A fast and reasonably accurate numerical three‐dimensional wake model able to predict the flow behaviour of a wind farm over a flat terrain has been developed. The model is based on the boundary‐layer approximation of the Navier–Stokes equations, linearized around the incoming atmospheric boundary layer, with the assumption that the wind turbines provide a small perturbation to the velocity field. The linearization of the actuator‐disc theory brought additional insights that could be used to understand the behaviour, as well as the limitations, of a flow model based on linear methods: for instance, it is shown that an adjustment of the turbine's thrust coefficient is necessary in order to obtain the same wake velocity field provided by the actuator disc theory within the used linear framework. The model is here validated against two independent wind‐tunnel campaigns with a small and a large wind farm aimed at the characterization of the flow above and upstream of the farms, respectively. The developed model is, in contrary to current engineering wake models, able to account for effects occurring in the upstream flow region, thereby including more physical mechanisms than other simplified approaches. The conducted simulations (in agreement with the measurement results) show that the presence of a wind farm affects the approaching flow far more upstream than generally expected and definitely beyond the current industrial standards. Despite the model assumptions, several velocity statistics above wind farms have been properly estimated providing an insight into the transfer of momentum inside the turbine rows. Copyright © 2016 John Wiley & Sons, Ltd.

Wind Farm Blockage and the Consequences of Neglecting Its Impact on Energy Production

“…We do, however, have reason to believe that the wind farms could cause such consistently observed slowdowns. Separate wind tunnel and LES studies have shown such an effect [12][13][14], and the RANS results herein, which absolutely isolate wind farm impact, include upstream slowdowns that are reasonably consistent with average measured ∆U P,R , whether binned by distance upstream or by wind farm. We therefore conclude that the presence of the wind farms is very likely the primary cause behind the significant wind speed reductions observed at the perimeter masts after COD.…”

“…Yet the literature also includes indications of potential shortcomings in the wakes-only approach. In Ebenhoch [12], wind tunnel measurements and corresponding model predictions revealed a wind speed deficit upstream of a 105-turbine wind farm. The deficit was much larger and Consistent with this approach, research on the fluid dynamic interaction between turbines has, until recently, focused almost exclusively on wakes.…”

Linearized simulation of flow over wind farms and complex terrains

“…As the model was developed to account for both topography and turbines, it enables both features to be combined and some of the limitations of the current industrial assumptions to be assessed. In order to quantify the effect of topography in wind farms, a three-dimensional simulation was done with a wind farm composed of 10 rows in a staggered arrangement (10 turbines followed by 11 turbines, for a total of 105 turbines), replicating the experiments performed in the Gävle wind tunnel and described in [11,19]. The spacing between the rows was S x = 4D, while the spacing between the turbines in the lateral direction was S y = 2.66D, where D = 45 mm is the turbine diameter (the hub height was z hub = 60 mm).…”

“…This will lead to a significant error in the estimated velocity near the rotor (although the velocity magnitude might change inside the cylinder volume, something that does not happen in an actuator disc), but it should not significantly affect the far field. Owing to the limited number of points inside the actuator-disc volume (there should be N p = 3 − 4 points inside each volume, depending on the relative position between the grid and the turbine, so that turbines should not introduce sudden impulses), a multiplicative correction factor of 2δ/(N p x) was introduced in equation (2.9) to compensate for the finite number of points inside the cylinder, as discussed in [11]. Figure 4 shows the comparison between the streamwise velocity of the three cases evaluated in a horizontal plane at constant height from the ground, η = z hub /D.…”

“…Recent studies [10,11] have indicated that these linearized models are reliable for the mean streamwise velocity and Reynolds shear stress, but they provide poor results for the turbulent kinetic energy (TKE)-at least over forested areas, where the TKE increases by a factor of order O (10) and the linearity assumption becomes invalid. Therefore, the effect of nonlinearities is very important in turbulence transport and generation, suggesting that the full nonlinear equations should be used as the only possibility to gain information about the mean flow and the TKE, simultaneously.…”