This paper presents grid adaptive Reynolds-averaged Navier-Stokes (RANS) simulations of turbulent jet injection in subsonic crossflow. Three different velocity ratios, which are commonly encountered in film cooling and combustion applications, are considered. The simulations are performed using a well-validated flow solver and an eddy viscosity model. Detailed comparisons with experimental data are illustrated and an evaluation of the suitability of the turbulence model is discussed. Furthermore, a practical grid adaptation strategy is shown to provide a way to resolve the flow features without requiring drastic increase in the number of cells. The results demonstrate the usefulness of grid adaptation as well as represent a contribution to understanding the capability and limitations of RANS turbulence models in predicting turbulent jet injection in crossflow.