Extrapolability and limitations of a semi-empirical model for the simulation of volumetric expanders

Many different modelling approaches can be used to simulate the performance of expansion devices in ORC power systems. A decade ago, researchers proposed a semi-empirical modelling method that can be used to generally characterize volumetric expanders (e.g. scroll, screw, piston or vane machines). The modelling approach relies on a limited number of physically meaningful equations which decompose the expansion process into a number of consecutive steps. Besides of under- and over-expansion losses (due to the fixed built-in volumetric ratio of the machine), the model can account for pressure drops at the inlet and outlet ports, internal leakages, mechanical losses, recompression effects and heat losses to the environment. The semi-empirical model relies on different parameters that must be properly tuned according to experimental (or manufacturer) data. In practice, the reference database used for the parameters calibration (e.g. the measurements gathered on a test rig) does not necessarily cover the entire range of conditions onto which the model will be evaluated. The capability of the semi-empirical model to behave well in extrapolated conditions must therefore be assessed. In this work, a detailed analysis of the extrapolation performance of this semi-empirical model is conducted. More specifically, the semi-empirical model behavior is analyzed after being calibrated with different ranges of reference conditions. A study of the smallest reference dataset to ensure a decent modelling accuracy is proposed. Finally, the influence of the parameters guess values and the optimization algorithm on the model calibration is assessed.