Transition to bluff-body dynamics in the wake of vertical-axis wind turbines

Abstract

We present experimental data to demonstrate that the far wake of a vertical-axis wind turbine (VAWT) exhibits features that are quantitatively similar to that of a circular cylinder with the same aspect ratio. For a fixed Reynolds number ($Re\approx 0.8\times 10^{5}$) and variable tip-speed ratio, two-dimensional particle image velocimetry (PIV) is used to measure the velocity field in the wake of four different laboratory-scale models: a 2-bladed, 3-bladed and 5-bladed VAWT, as well as a circular cylinder. With these measurements, we use spectral analysis and proper orthogonal decomposition (POD) to evaluate statistics of the velocity field and investigate the large-scale coherent motions of the wake. In all cases, we observe three distinct regions in the VAWT wake: (i) the near wake, where periodic blade vortex shedding dominates; (ii) a transition region, where growth of a shear-layer instability occurs; (iii) the far wake, where bluff-body wake oscillations dominate. We define a dynamic solidity parameter, $\unicode[STIX]{x1D70E}_{D}$, that relates the characteristic scales of the flow to the streamwise transition location in the wake. In general, we find that increasing $\unicode[STIX]{x1D70E}_{D}$ leads to an earlier transition, a greater initial velocity deficit and a faster rate of recovery in the wake. We propose a coordinate transformation using $\unicode[STIX]{x1D70E}_{D}$ in which the minimum velocity recovery profiles of the VAWT wake closely match that of the cylinder wake. The results have implications for manipulating VAWT wake recovery within a wind farm.