CFD analyses of two benchmark, two-dimensional, sinusoidally oscillating, turbulent flows (one with zero mean and one with nonzero mean) at relatively large Reynolds and Keulegan-Carpenter numbers and relative current velocities, have been performed with CFD-ACE, a Favre-averaged Navier-Stokes (FANS) code. The primary purpose of the investigation was a critical assessment of the computational accuracy of time-dependent turbulent flows with large-scale unsteadiness. A number of turbulence models, including the standard k -ε, re-normalization group (RNG) based k -ε, and low-Reynolds number model have been employed. Among others, a second order in time, second order in space, second-level predictor-corrector finite-difference scheme has been used. The analysis produced the time-dependent in-line and transverse forces, the force coefficients, instantaneous velocity, vorticity, and pressure distributions, and streamlines. Representative results are compared with each other and with those obtained experimentally.