Evaluate the validity of the empirical correlations of clearance and friction coefficients to improve a scroll expander semi-empirical model

Abstract

This study presents a scroll expander modelling methodology for small scale power generation systems by combining scroll geometry and semi-empirical model. Although the semi-empirical model is quite popular, its dependence on several experimentally-determined scroll geometrical and operational parameters makes this approach inflexible for different capacities and operating conditions. Some studies have sought to improve its flexibility in terms of using different working fluids and more accurate empirical parameters, however, those improved models still depend on a considerable number of experimentally-obtained scroll parameters. Therefore, in this study, a practical methodology for a simpler semi-empirical model combined with the operational flexibility of the scroll geometry is presented. Firstly, the flow rates of mainstream and leakage flows are analysed, where a correlation between scroll clearance and pressure ratio is determined. Secondly, a simpler approach to the semi-empirical model of scroll expander is proposed, whereby dependent parameters have been reduced to two parameters by using scroll geometrical calculations. The model is further improved to predict the rotational speed and electricity output by considering the overall friction coefficient of the coupled expander-generator unit. The findings are then compared with the results of an experimental study. The results show that the effective clearance values between scrolls vary according to pressure ratios, increasing from 20μm to 34μm. Mass flow rate can be predicted within 10% deviation from the experimental results for the same inlet conditions and rotational speed at a transient state. Additionally, considering steady state conditions, modelling results show that the rotational speed and electricity output can also be predicted within 8% and 7.5% of deviation, respectively.