Modeling the influence of streamwise flow field acceleration on the aerodynamic performance of an actuator disk

Wind turbines operating in complex terrain can be subject to a background flow field that varies in the streamwise direction. This variation can influence the induced velocity at the turbine and thus also the power performance. In the present work, a simple model is derived for the situation of an actuator disk (AD) operating in a background flow field featuring a constant streamwise velocity gradient. Reynolds-averaged Navier–Stokes (RANS) simulations of this scenario are performed, showing that a positive acceleration yields a reduction of induction, while a negative acceleration leads to an increase in induction. The new model accurately captures this behavior and significantly reduces the prediction error compared to classical momentum theory, where the effect of the background flow acceleration is disregarded. The model indicates that the maximum power coefficient and the corresponding values of the optimal induction and thrust coefficient depend on the flow acceleration. This possibly impacts optimal operational strategies under such conditions as well as wind turbine and wind farm design considerations, which often rely on the assumption of a streamwise uniform flow field.