A Simple Model for Wake-Induced Aerodynamic Interaction of Wind Turbines

Abstract

Wind turbine aerodynamic interactions within wind farms lead to significant energy losses. Optimizing the flow between turbines presents a promising solution to mitigate these losses. While analytical models offer a fundamental approach to understanding aerodynamic interactions, further development and refinement of these models are imperative. We propose a simplified analytical model that combines the Gaussian wake model and the cylindrical vortex induction model to evaluate the interaction between wake and induction zones in 3.5 MW wind turbines with 328 m spacing. The model’s validation is conducted using field data from a nacelle-mounted LiDAR system on the downstream turbine. The ‘Direction to Hub’ parameter facilitates a comparison between the model predictions and LiDAR measurements at distances ranging from 50 m to 300 m along the rotor axis. Overall, the results exhibit reasonable agreement in flow trends, albeit with discrepancies of up to 15° in predicting peak interactions. These deviations are attributed to the single-hat Gaussian shape of the wake model and the absence of wake expansion consideration, which can be revisited to improve model fidelity. The ‘Direction to Hub’ parameter proves valuable for model validation and LiDAR calibration, enabling a detailed flow analysis between turbines. This analytical modeling approach holds promise for enhancing wind farm efficiency by advancing our understanding of turbine interactions.