Simplified modeling of wind-farm flows

University essay from KTH/Strömningsfysik

Abstract: Abstact: In order to address the wind-industry's need for a new generation of more advanced wake models, which accurately quantify the mean flow characteristics within a reasonably CPU-time, the two-dimensional analytical approach by Belcher et al. (2003) has been extended to a three-dimensional wake model. Hereby, the boundary-layer approximation of the Navier-Stokes equations has been linearized around an undisturbed baseflow, assuming that the wind turbines provoke a small perturbation of the velocity field. The conducted linearization of the well established actuator-disc theory brought valuable additional insights that could be used to understand the behavior (as well as the limitations) of a model based on linear methods. Hereby, one of the results was that an adjustment of the thrust coecient is necessary in order to get the same wake-velocity field within the used linear framework. In this thesis, two different datasets from experiments conducted in two different wind-tunnel facilities were used in order to validate the proposed model against wind-farm and single-turbine cases. The developed model is, in contrary to current engineering wake models, able to account for effects occurring in the upstream flow region. The measurement, as well as the simulations, show that the presence of a wind farm affects the approaching flow even far upstream of the first turbine row, which is not considered in current industrial guidelines. Despite the model assumptions, several velocity statistics above wind farms have been properly estimated, providing insight about the transfer of momentum inside the turbine rows. Overall, a promising preliminary version of a wake model is introduced, which can be extended arbitrarily depending on the regarded purpose.

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