The impact of secondary flows on the flow velocity in open channel bends and confluences was simulated using three-dimensional (3D) numerical models. The Reynolds-averaged Navier–Stokes equation system was utilized as the governing equations and two different turbulence models were employed in this study: the standard k-ε model and the realizable k–ε model. In a recent study by the authors, the rigid lid approach was used, which does not allow for vertical displacement of the water surface. In this study, the simulation of free surface displacements was simulated using the volume of fluid free-surface tracking method. The numerical models were evaluated and validated by using the experimental data of a sharply curved channel and a confluent channel. The accuracies of the two turbulence models were evaluated and discussed. This study found that both models can satisfactorily reproduce the experimental data. However, the standard k–ε model performed better for the curved channel case while the Realizable k–ε model performed better for the confluent channel case.