Flows around sets of airfoils with different shapes and thicknesses have been numerically investigated at the relatively high Reynolds number (Re ≥ 106) and the low turbulence intensity (I ≤ 0.1 %) using two-dimensional (2D) Reynolds Averaged Navie-Stokes equations (RANS) in the combination with different semi-empirical turbulence models. The effects of different factors such as wind tunnel walls, the compressibility and the influence of the laminar-turbulent transition were investigated. The most probable reasons for the systematic disagreement between simulation and experimental data were established to be 3D effects impossible to be taken into account within 2D simulation or imperfection of the present-day semi-empirical turbulence models.