Due to the high Reynolds numbers together with the complex turbulent motions in turbomachinery, selecting a proper turbulence-modeling method is of vital significance in interpreting the real flow physics. In this paper, shear stress transport (SST) as a Reynolds-averaged Navier–Stokes model and scale-adaptive simulation (SAS) and zonal large eddy simulation (ZLES) as two scale-resolving simulation approaches were chosen to simulate the flow in a low-speed axial compressor rotor at three different blade tip clearances (1.3, 2.6, and 4.3% of chord length). Results of unsteady simulations at the design point were compared to the experimental data. The results prove that the ZLES model performs best in characterizing the experimental data regardless of the blade tip clearance size. The performance of the SST model in capturing the tip flow is close to the measurement data when the blade tip clearance is small, while the deviation from the experimental results increases with the clearance size enlarged. In contrast, the use of the SAS model does not result in any benefits over the SST model for the small tip clearance but demonstrates similar performance with the ZLES model for the configurations with middle and large tip clearance sizes.