The three-dimensional turbulent flow field in unbaffled tanks stirred by radial impellers was numerically simulated by a finite-volume method on body-fitted, co-located grids. Simulations were run, with no recourse to empirical input, in the rotating reference frame of the impeller. Free-surface problems were also simulated, in which the profile of the central vortex was computed as part of the solution by means of an iterative technique. Predicted velocity and turbulence fields in the whole vessel and power consumptions were assessed against available literature data; free-surface profiles were also compared with original experimental data obtained in a model tank. Both the eddy-viscosity k-epsilon turbulence model and a second-order differential stress (DS) model were used and compared : satisfactory results were obtained only by using the latter model. The need for including source terms arising from fluctuating Coriolis forces in the Reynolds stress transport equations is highlighted.