Finite-volume numerical simulations of the flow field in a curved-bottom; free-surface reactor are presented. Full transient simulations with explicit modeling of the air-water interface are made in order to reproduce correctly the entire flow field in the vessel. Qualitative comparison of numerical results is given against literature and experimental data. We discuss critically the measurements of the extent of transient duration for the different simulations, and of the axial flowrate. Furthermore, we try to evaluate the importance of the free-surface deformation. In order to evaluate this, we calculate the energy required to shape the free surface, which we find to be up to 6% of the fluid kinetic energy. Finally, we evaluate the stirring capability of the reactor in different working conditions.