Improving the semi-empirical modelling of a single-screw expander for small organic Rankine cycles

The common semi-empirical modelling adopted for positive-displacement rotary expanders is revised in this paper. Paying particular attention to the leakage flow rates, the mechanical losses at the shaft and the ambient heat losses by the proposal of a more physically sound modelling, this paper aims at improving the performance simulation of a single-screw expander for which there exists a wide experimental campaign in literature. In detail, the mechanical losses are modelled with an approach consistent with the Stribeck's theory, whereas the contributions of both natural convection and radiation are taken into account for a proper modelling of the ambient heat losses. After calibration and validation of the modelling procedure, based on experimental data of the expander operation with R245fa, mean absolute percentage errors of 0.69%, 1.77% and 0.33% as regards mass flow rate, electric power output and exhaust fluid temperature, respectively, are calculated. These errors are lower than the ones reported by other researchers, so the current simulations are more consistent with the experimental data. Considering the higher reliability for a better performance simulation by the new modelling procedure, the model is finally used to study the behavior of the expander. In particular, attention is paid to the mass flow rate, the shaft and the electric power outputs, the expander efficiency, as well as the ambient heat losses, and to their relations with the operation parameters such as the degree of fluid superheat at the expander inlet, the fluid pressure at the expander inlet, the pressure ratio and the rotational speed.