This paper presents a systematic comparison of ejector performance predictions by a thermodynamic and a CFD model for different operating conditions. The thermodynamic model developed by Galanis and Sorin (2015) assumes the primary flow is always choked, and irreversibilities due to viscous dissipation are taken into account through polytropic efficiencies. The CFD model developed by Croquer et al. (2015) using the software ANSYS Fluent v15.0 has already been validated for supersonic ejectors working with R134a. A standard high Reynolds number k- ω SST turbulence model coupled with the perfect gas law is used to model the turbulent air flows. The dimensions of the ejector were first determined by the thermodynamic model and then used in the CFD model. The thermodynamic model predicts higher entrainment ratios for double choking operation and somewhat different values of the critical and limiting pressure ratios. The CFD model validates the similarity solutions characteristic of ejectors using perfect gases. The present results show in particular that identical inlet pressure and temperature ratios induce the same entrainment ratio as well as the same critical and limiting pressure ratios. Both models confirm also that similar diameter ratios between the primary nozzle throat and the constant area section lead to the same values of the entrainment ratio. Thus, for double-choking operations, the entrainment ratio depends on the inlet pressure and temperature ratios rather than on the individual values of these four properties as is the case for ejectors with real fluids. It also shows that the position of the shock varies linearly with the compression ratio in qualitative agreement with the assumption used in the thermodynamic model. Finally, the main assumptions made to build the thermodynamic model have been checked and discussed a posteriori using the CFD results