Effects of hydrofoil shape and turbine solidity on the wake energy recovery in cross-flow turbines

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 the literature. By means of 3D Unsteady Reynolds Averaged Navier-Stokes (URANS) simulations and a momentum budget simplified approach, this author investigated the effects of blade profile and turbine solidity on the blade tip vortex generation and then on the mixing mechanisms supporting the reintroduction of streamwise momentum into the wake. Results indicate that: (a) pairs of counter-rotating vortices occurs in the wake, which rotation direction depends on blade profile and it is such as to generate positive vertical advection for camber-out profiles, but negative vertical advection 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.