Numerical study on the spontaneous condensation flow in an air cryogenic turbo-expander using equilibrium and non-equilibrium models

•We study the air spontaneous condensation in a cryogenic turbo-expander.•Using non-equilibrium model to supply the details of flow characteristics.•Three types of expansion in turbo-expander are summarized.•Comparison of equilibrium and non-equilibrium models is given.•The influence of wetness on turbo-expander efficiency is analyzed.