In this article, single-phase, computational-fluid-dynamics simulations of free-surface vortices are presented. The purpose of the simulations is to determine the appropriate turbulence model for free-surface vortices, which could later be applied to simulations of flow in various engineering systems. The water flow in the laboratory model of a free-surface vortex was numerically simulated by unsteady single-phase computations. The vortex circumferential velocity, the downward velocity inside the vortex core and the predicted length of the free-surface vortex gas core were compared with available measurements. For the two-equation turbulence models, the results indicated the importance of the curvature correction (CC). The effect of the time-step size and the choice of the advection scheme were analyzed. For the tested case, it was determined that the unsteadiness of the flow was insufficient for the correct behavior of the scale-adaptive simulation (SAS) turbulence model. With the CC option, the shear-stress-transport (SST-CC) turbulence model and the SAS-CC turbulence model can both be used for such predictions; however, the SAS-CC model was found to be more reliable. Single-phase simulations successfully predicted the gas-core length for vortices with a short gas core. However, for long cores, the length was underpredicted.