Fluid dynamic mechanisms for the wake energy recovery in cross-flow turbines: effects of hydrofoil shape and turbine solidity

Cross-flow turbines (CFTs) are arousing a growing interest to harvest both off-shore wind and tidal currents. A promising characteristic of CFTs could be a high power-density in case of multi-device clusters or farms, achievable by shortening the distance between arrays as allowed by the fast energy recovery observed inside the wakes. However just few studies, only concerning symmetrical airfoils/hydrofoils, are found in literature. By means of 3d-URANS simulations and the momentum budget approach we investigated the effects of blade profile and turbine solidity on blade tip vortex generation and then on the mixing mechanisms supporting the reintroduction of streamwise momentum into the wake. Results indicate that: (a) a pair of counter-rotating vortices occurs in the wake at the turbine top and bottom ends, which rotation verse depends on blade profile and it is such as to generate positive vertical advection for camber-out profiles, but negative vertical dvection for camber-in profiles; (b) camber-out profiles are much more effective in supporting the wake energy recovery due to the massive vertical advection induced by tip vortices; (c) for camber-in profiles the tip vortices poorly contribute to the wake recovery, that appears delayed and promoted by turbulent transport; (d) higher solidity implies stronger tip vortices and higher turbulent transport, therefore a faster wake recovery.