The present work is dedicated to the study of cryogenic nitrogen jets under supercritical chamber conditions with the objective of simulating the process of fuel injection inside a combustion engine. In order to do so, a numerical simulation using a RANS model was performed over two case studies previously analyzed by other authors both in experimental and numerical studies. The result obtained by the present numerical approach were then compared with previous results and this way accessed the capabilities of RANS approach using a k-ε turbulence model in which the density is calculated through the mixture fraction value to correctly model cryogenic jets at supercritical conditions. The results show the ability to achieve good agreement with other studies for the axial density distribution however for other parameters like the jet spreading angle the same agreement was not found.