In this paper, 3D Navier-Stokes simulations of the unsteady flow over the NREL Phase VI turbine are presented. The computations are carried out using the structured grid, incompressible, finite volume flow solver EllipSys3D, which has been extended to include the use of overset grids. Computations are presented, firstly, on an isolated rotor, and secondly, on the downwind configuration of the turbine, which includes modelling of the rotor, tower and tunnel floor boundary.The solver successfully captures the unsteady interaction between the rotor blades and the tower wake, and the computations are in good agreement with the experimental data available. The interaction between the rotor and the tower induces significant increases in the transient loads on the blades and is characterized by an instant deloading and subsequent reloading of the blade, associated with the velocity deficit in the wake, combined with the interaction with the shed vortices, which causes a strongly time-varying response. Finally, the results show that the rotor has a strong effect on the tower shedding frequency, causing under certain flow conditions vortex lock-in to take place on the upper part of the tower.