The purpose of this investigation is to study the supercritical and transcritical injection of cryogenic fluids by means of a Computational Fluid Dynamics analysis using a RANS approach and different turbulent Prandtl number models. Besides, with the aid of the differential equation for entropy, the local entropy generation is pursued. Using this method, the areas where the irreversibilities occur are detected, and the mechanisms concerning entropy generation identified. The novelty of the numerical procedure presented herein is the use of two different turbulent Prandtl number (Pr-T) models that affect strongly the result produced: a constant Pr-T and a molecular dependent Pr-T. The main results show that the constant Pr-T predicts better the flow structure when compared to experimental data, being Pr-T = 0.5 the optimum one. This result suggest that supercritical and transcritical fluid injection are more dissipative processes than normal pressure injection, where Pr-T approximate to 1. (C) 2016 Elsevier B.V. All rights reserved.