Spatial development of planar and axisymmetric wakes of porous objects under a pressure gradient: a wind tunnel study

Abstract. We report an experimental study on the effect of a constant adverse pressure gradient on the spatial evolution of turbulent wakes generated by different objects. A porous disk, designed to mimic the wake of a horizontal axis wind turbine, and a porous cylinder, whose wake matches that of a vertical axis wind turbine, were tested in a wind tunnel for Reynolds numbers (based on the generator diameter) in the range of 2.6 × 10⁵ to 3.9 × 10⁵. Experiments were conducted between 1 and 7 diameters downstream of the disk and from 2 to 12 diameters downstream of the cylinder.

We find that the effect of the pressure gradient is significant in all cases, resulting in larger velocity deficits and wider wakes. Moreover, these variations are stronger for the cylinder-generated wake. We also find that current analytical models for wakes evolving in pressure gradients, developed from momentum conservation, satisfactorily fit our data. Our results provide a benchmark case that will contribute to improving energy harvesting in cases where pressure gradients are relevant, such as in wind plants installed over complex topographies and tidal stream generators.