In the current work, we perform numerical simulations of the phase change process of Carbon Dioxide inside three different converging diverging nozzles, the experimental data on which is available in open literature. The simulations are performed with the classical nucleation theory based non-equilibrium phase change solver available in Ansys CFX with the thermophysical properties of CO₂ obtained from NIST Refprop. We focus on the supercooling levels attained by the fluid and the distribution of the liquid mass fraction of CO₂ during its high speed expansion inside the nozzles. The nozzle shape, expansion rate and fluid inlet conditions have a strong influence on the supercooling levels and the maximum liquid mass fractions obtained inside the nozzles. The results show much lower supercooling levels attained by CO₂ (~ 2K) inside the Claudio Lettieri nozzle, the inlet state for which is near to the critical point. The supercooling attained by the vapor inside the Gyarmathy nozzle is around 22.5 K, the inlet state for which is far from the critical point. The case with the Nakagawa nozzle fails to converge properly.