This paper presents computational fluid dynamics (CFD) simulations of the flow around a horizontal axis hydrokinetic turbine (HAHT) found in the literature. The volume of fluid (VOF) model implemented in a commercial CFD package (ANSYS-Fluent) is used to track the air-water interface. The URANS SST k-ω and the four-equation Transition SST turbulence models are employed to compute the unsteady three-dimensional flow field. The sliding mesh technique is used to rotate the subdomain that includes the turbine rotor. The effect of grid resolution, time-step size, and turbulence model on the computed performance coefficients is analyzed in detail, and the results are compared against experimental data at various tip speed ratios (TSRs). Simulation results at the analyzed rotor immersions confirm that the power and thrust coefficients decrease when the rotor is closer to the free surface. The combined effect of rotor and support structure on the free surface evolution and downstream velocities is also studied. The results show that a maximum velocity deficit is found in the near wake region above the rotor centerline. A slow wake recovery is also observed at the shallow rotor immersion due to the free-surface proximity, which in turn reduces the power extraction.