A new analytical model for wind-turbine wakes

• A new analytical model is proposed to predict wind velocity in turbine wakes.
• Conservation of mass and momentum are applied to derive the model.
• A Gaussian distribution is assumed for the velocity deficit in the wake.
• This simple model only requires one parameter to predict the wake velocity.
• Model results agree well with wind-tunnel measurements and large-eddy simulations.

A new analytical wake model is proposed and validated to predict the wind velocity distribution downwind of a wind turbine. The model is derived by applying conservation of mass and momentum and assuming a Gaussian distribution for the velocity deficit in the wake. This simple model only requires one parameter to determine the velocity distribution in the wake. The results are compared to high-resolution wind-tunnel measurements and large-eddy simulation (LES) data of miniature wind-turbine wakes, as well as LES data of real-scale wind-turbine wakes. In general, it is found that the velocity deficit in the wake predicted by the proposed analytical model is in good agreement with the experimental and LES data. The results also show that the new model predicts the power extracted by downwind wind turbines more accurately than other common analytical models, some of which are based on less accurate assumptions like considering a top-hat shape for the velocity deficit.

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