Fully developed turbulent flow in a concentric annulus with one or both walls rotation is essential in various engineering applications, such as heat exchangers, chemically reactive mixers, journal bearings and turbomachinery. Over the past decades, various DNS and LES studies were performed to provide a better understanding of the concentric annulus-related turbulence and the rotating effect on the turbulence structures. However, even large-eddy simulations (LES) are deemed to be barely feasible due to excessive resolution requirements in the case of near-wall viscous processes, which influence the main flow properties in the present configuration. The traditional RANS second-moment closure model, similar as other RANS models, with its deficiency in accuracy originating from its time-averaged theoretical rationale, produces results restricted to mean flow properties and second-order statistics without insight into flow patterns or turbulence structures. Based on the implementation within the framework of the OpenFOAM numerical code, turbulent flow in a concentric annulus with a rotating inner or outer cylinder wall was simulated by applying a differential near-wall Reynolds stress model employed within a conventional RANS (Reynolds-Averaged Navier-Stokes) framework and its unsteady eddy-resolving version to elucidate the effect of wall rotation on the near-wall structure.