This study deals with the three-dimensional unsteady numerical simulation of the flow around a cross-flow vertical-axis water turbine (CFWT) of the Darrieus type. The influence of turbine design on its hydrodynamic characteristics and performance is investigated by means of a time-accurate Reynolds Averaged Navier Stokes (RANS) commercial solver. The flow unsteadiness is described using a transient rotor-stator model in connection with a sliding interface. A classical Darrieus straight blade turbine, based on the NACA0025 airfoil, has been modified adding winglets (symmetric and asymmetric designs) to the blades’ tips with the objective of reducing the strength of the detached trailing vortices. The turbulent features of the flow have been modelled by using different turbulence models (k-ε Renormalization Group, standard Shear Stress Transport, transition Shear Stress Transport and Reynolds Stress Model). As a result, the predicted hydrodynamic performance of the turbine including winglets increases, independently of the employed turbulence model, being the improvement higher when a symmetric winglet design is considered. Moreover, visualization of skin friction lines pattern and their connection with vorticity isosurfaces, illustrating the flow detachment in the three blade configurations, has been carried out. Finally, a short discussion about the intermittency behavior along a turbine revolution is presented.