The chamber model method is still a powerful tool for the thermodynamic simulation of screw machines and is widely used in the industry and in science. When choosing adequate submodels for the compressible flows through machine clearances and the machine ports high simulation accuracy can be reached with minimal computation resources. However, detailed modelling is required when the complex geometry of twin-screw machines is abstracted to a time-dependent zero-dimensional chamber model. In this paper a two-chamber model simulation tool is used for the thermodynamic simulation of an oil-free twin-screw expander operating with dry air as working fluid. Insights into the modelling process are presented and the importance of precise modelling of gap flows between adjacent capacities is discussed. The simulation results are finally validated against experimental data. Integral values obtained from the experiments, such as expander mass flow rate, indicated power, and effective power, are in good agreement with the numerical calculations. To gain a deeper understanding of the thermodynamics of the expander working cycle, additional investigations are carried out at zero speed. The mass flow rates measured for a variation of stationary rotor positions are compared to values calculated with the two-chamber model method.