In the China initiative Accelerator Driven System (CiADS) project, a 2.5 MW lead–bismuth eutectic (LBE) cooled spallation target is planned to be constructed. The heat deposited in the spallation reactive zone and the hemi-spherical window is removed by convective LBE flow. The target window is a crucial component of the spallation target and its temperature distribution needs accurate evaluation by numerical simulation since experimental measurement is extremely difficult. In this study, in order to investigate the heat transfer characteristics between convective LBE flow and a hemi-spherical target window, computational fluid dynamics (CFD) simulation was performed for the simplified flow channel and target window with a constant heat flux boundary condition. Due to the special heat transfer properties of LBE, turbulent Prandtl number models for liquid metal were embedded in the Reynolds-averaged Navier–Stokes (RANS) models, while Large Eddy Simulation (LES) was performed in parallel. The Reynolds number ranges from 90,000 to 230,000 depending on the size of the window. The average Nusselt numbers of the target window obtained in simulation were compared with existing correlations. Results indicate that the average Nusselt numbers in RANS simulation are all significantly larger than those obtained by LES. Obvious deviations between simulation results of this study and the correlations reported in the literature are observed. The applicability of existing turbulent Prandtl number models in RANS thus needs further evaluation and verification. Results obtained in this study will be utilized for future development of turbulent Prandtl number models, which are capable of calculating the heat transfer behavior between liquid metal flow and hemi-spherical configurations accurately.