The paper presents a numerical investigation of the flow around a NACA23012 airfoil with two ice shapes, a spanwise ridge and leading edge roughness. RANS and URANS simulations are completed with various 1 st and 2 nd order turbulence models (Spalart-Allmaras, Menter SST, EARSM, DRSM) for a selected number of points of the airfoil polar. To assess the ability of advanced unsteady hybrid RANS/LES models, one selected flow condition of the spanwise ridge case is also computed with a ZDES hybrid method. The results are compared with experimental data (integrated loads, pressure distribution, velocity field) obtained in the ONERA F1 wind tunnel. The Spalart-Allmaras model is the only RANS model among those assessed in this study converging efficiently towards steady-state whatever the flow condition considered. Together with DRSM, it also provides a reasonable predictive effect on the performance degradation due to ice shape. DRSM is much more expensive as it contains more physics, providing natural unsteady solutions which have to be time-averaged. DRSM first and second-order statistic fields compare well with ZDES ones, both of them indicating that geometrical three-dimensionality of the ice shapes should be taken into account. Furthermore, the unsteady content of the DRSM URANS solution is compared with that of ZDES, showing that the vortex shedding phenomenon can also be captured by DRSM.