Time-varying wind-turbine wakes at high Reynolds numbers

TL;DR

This study investigates how slow, time-varying flow conditions affect wind-turbine wake dynamics at high Reynolds numbers, revealing that wake advection and wave propagation influence wake behavior and can be controlled for improved wind-farm performance.

Contribution

It demonstrates that wake advection at high Reynolds numbers can be modeled with a Lagrangian transformation, enabling better control and understanding of wake dynamics under time-varying conditions.

Findings

Wake disturbances propagate as traveling waves.

Wake advection velocity matches wake velocity, not free stream.

Time-varying control can optimize wind-farm performance.

Abstract

Wind turbines operating in the atmospheric boundary layer are constantly exposed to time-varying flow conditions. These disturbances often occur on similar time scales to wind-turbine controllers, which may interfere with wind-farm control strategies that operate under steady-flow assumptions. This study aims to investigate the significance of such time variations on wind-turbine wake dynamics, focusing on slow time scales representative of quasi-steady processes in large wind farms. Experiments are conducted at near utility-scale Reynolds numbers ($Re_D=4\times10^6$) in a pressurized-air wind tunnel, with a wind turbine forced in periodic rotation-rate oscillations by means of a time-varying generator torque at low Strouhal numbers ($St=0.04$). Flow measurements in the wake of the turbine demonstrate that disturbances propagate through the wake as traveling waves, which are advected nonlinearly at the velocity of the wake rather than that of the free stream. The wake behavior can be described in a quasi-steady manner, but only after wake advection is accounted for by a Lagrangian transformation. Even in the quasi-steady regime, the spatiotemporal evolution of the wake can be controlled by independently varying the turbine thrust and tip-speed ratio. The results suggest that wake advection is important to consider for wind-farm modeling and control, and that time-varying control may allow wind-turbine wake interactions to be tuned even in nominally quasi-steady conditions for optimal wind-farm performance.