Over the last decade, Carbon dioxide (R744) a natural fluid has gained significant interest as a potential substitute for synthetic refrigerants commonly used in refrigeration, air-conditioning, and heat pump systems. Because of CO2 properties, such cycles generally operate in transcritical conditions. Moreover, their Coefficient Of Performance (COP) is relatively low compared to conventional cycles using synthetic refrigerants, because of higher entropy production of C02 along an isenthalpic expansion from a supercritical state to a subcritical state. Integrating a two-phase ejector, as an expansion device, is a promising technology to significantly improve the system efficiency, which would make CO2 adequate for HVAC applications. For example, in a CO2 ejector-expansion system, an ejector replaces the classical throttling valve to partly recover the throttling losses and provides a compression work reducing the compressor load. As a result, the COP and cooling capacity can be improved. However, many complex physical phenomena occur within a two-phase CO2 ejector and they are not yet fully understood, such as the turbulent mixing between the primary and the secondary flows, the flashing in the primary nozzle, shock waves-shear layer interactions, as well as phase-change processes. In this thesis, a numerical approach was developed by combining an efficient look-up table method for CO2 properties, density-based solvers, and characteristic Navier-Stokes boundary conditions (NSCBC) in order to correctly predict those complex flow features. This look-up table method allows to compute vapor, liquid, supercritical and two-phase properties of CO2 from 217K to 1000K and pressures up to 50MPa. It was coupled to three density-based solvers which allow to perform inviscid simulations, Reynolds-Averaged Navier-Stokes Simulations (RANS), and Large-Eddy Simulations (LES). Validations and verifications were performed for these three solvers. Then, Converging-diverging nozzles and ejectors were investigated by using RANS simulations. The developed solver was used to conduct an exergy tube analysis for a two-phase CO2 ejector and the sensibility of the method to the numerics was discussed. Finally, the compound-choking theory was extended for real gas flows and it was used to check the choking condition of the investigated ejector. (FSA - Sciences de l'ingénieur) -- UCL, 2019