Predicting the optimum design of single stage axial expanders in ORC systems: Is there a single efficiency map for different working fluids?

The variety of decision variables involved in the design of Organic Rankine Cycles (ORCs) and equipment still open opportunities to enhance efficiency and performance in the recovery of low grade and waste heat in spite of the high number of studies already available in the literature and the rapidly growing number of existing applications. Most of the literature focuses on cycle configuration, design parameters and working fluid that maximize different performance metrics, but often ignores the expander design features that are necessary to obtain them, by fixing in advance the expander efficiency. This approach is questionable for ORC systems where the high volumetric expansion ratios, variable sizes and working fluids may markedly affect expander efficiency. This study provides a design criterion of axial flow turbines which gives a reliable estimate of their efficiency for a wide range of operating duty specifications and working fluids. For fixed values of size parameter and volumetric expansion ratio the optimum values of duty parameters (flow and loading coefficients, degrees of reaction) and the associated turbine efficiency are obtained by a mean line design procedure including real gas properties and the recent loss correlations proposed by Aungier. For each working fluid, all the efficiency values obtained by this procedure for a wide set of size parameter and volumetric expansion ratio are included in a map, which updates a similar map obtained for high molecular weight ideal gases by Macchi and Perdichizzi in the eighties. A wide spectrum of working fluids and operating conditions is considered here to explore the effect of fluid characteristics on the shape of the efficiency maps. Results show that the influence of the working fluid on the efficiency maps may be not negligible, and can be taken into account by including the working fluid critical temperature in addition to the size parameter and volumetric expansion ratio. Accordingly, a generalized efficiency map is obtained which is valid for any fluid, and can be easily integrated into a comprehensive thermodynamic cycle analysis and optimization to account for the real turbine performance.