Injection and mixing of cryogenic propellants are very complex at near-critical and supercritical conditions. The concise description and the reliable measurements on such flows are still questionable. In this work, a Reynolds Averaged Navier-Stokes (RANS) study is performed for a pure N2 fluid injection at transcritical conditions on a laboratory scale test rig. An indepth thermodynamical analysis on the real-gas behavior has allowed N2 density prediction over the experimental range of the injection temperature and for several equations of state (EoS). A focus was thrown on the prediction of the density evolution on the chamber centerline and across the injector. The calculations were performed using both adiabatic and constant temperature conditions for the injector wall. The inner heat transfer in the injector had a significant effect on the jet density distribution and therefore on the overall flow dynamics. Numerical results regarding axial profiles of density and dense core lengths agree fairly well with the experimental data provided by the literature.