Pressure gradient effects on the wake of a model wind turbine in a turbulent boundary layer

Wind tunnel experiments were performed to study the effect of constant pressure gradients (PG) from the wall topography on the wake of a model wind turbine. Particle image velocimetry (PIV) was used to characterize the near and intermediate wake regions, whereas turbine power output was obtained at high temporal resolution. We explored five cases, including two favorable, two adverse pressure gradients, and a reference scenario with negligible pressure gradient. The result shows that pressure gradient induces a wake deflection and modulates the turbine wake; however, they imposed relatively small variations on turbulence kinetic energy and kinematic shear stress. This indicates a comparatively dominant effect of the bulk flow acceleration and deceleration on the flow recovery. Based on this, we propose a simple formulation. We first modeled the base flow profile over escarpments through a linearized perturbation method; the wake profiles are then acquired by solving the integral cross-stream streamwise momentum equation. It reasonably estimates the flow profile and PG-conditioned power output variations. This formulation can aid insight into wind-farm layout design in mild escarpment topographies.