Development of a thermodynamic low order model for a twin screw expander with emphasis on pulsations in the inlet pipe

A twin screw expander is a positive displacement machine used in various applications of waste heat recovery. The performance of this machine is influenced by internal leakages, gas pulsations formed in the inlet pipe and the properties of the refrigerant. In this paper a multi-chamber mathematical model of a twin screw expander is presented to predict its performance. From the mass and energy conservation laws, differential equations are derived which are then solved together with the appropriate Equation of State (EoS) in the instantaneous control volumes. In order to calculate the mass flow rates through leakage paths more accurately, flow coefficients used in the converging nozzle model were derived from 3D Computational Fluid Dynamic (CFD) calculation. Due to high gas pulsation levels at the inlet port, a coupling with a 3D CFD inlet pipe model is introduced in order to better predict throttling losses. The maximal deviation between predictions by the developed model and 3D CFD calculations of the complete machine is around 5% for the mass flow rate and the power output.