An experimental and analytical study of wind turbine wakes under pressure gradient

This work is dedicated to the systematic investigation of wind turbine wakes under the effect of pressure gradients. Wind tunnel experiments are carried out with a wind turbine positioned on straight ramps of increasing angle such that it experiences an approximately linear flow speed-up/slow-down from the induction region into the far wake. Fifteen ramp angles are studied: 7 favorable (FPG), 7 adverse (APG), and 1 zero pressure gradient. The wake center is shown to follow the base flow streamline originating from a virtual turbine hub height. A quasi-linear relationship between the pressure gradient and near wake length is demonstrated. Far wake characteristics, such as the recovery of the wake center velocity deficit and wake growth rate, are observed to systematically vary with the pressure gradient. The wake recovery rate increases (decreases) with the increase in the FPG (APG), and the wake growth rate shows a linear increase from most favorable to most adverse pressure gradient. The turbine power coefficient decreases significantly with increasing APG to a greater degree than the increase in power coefficient under FPG. The engineering approach of superposing the wake deficit predicted by the standard Gaussian model on the modified base flow is shown to work for very moderate pressure gradients. In light of this, a threshold in terms of flow speed-up/slow-down along the wake trajectory is established, below which the engineering approach can be reasonably employed. Finally, a physics-based model for wakes under the pressure gradient is tested. A new theoretical relation for near wake length under the pressure gradient is proposed. Using the theoretical near wake length, the pressure gradient model predicts the turbine wakes for all cases with good accuracy and shows a significant improvement from the engineering approach.