Preliminary design of organic fluid turbines to predict the efficiency

Turbine efficiency plays a key role in the design optimization of ORCs (organic Rankine cycles) and should be properly evaluated for an accurate estimate of the real power production. 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 turbine efficiency. This work focuses on the preliminary design of radial inflow turbines and single stage axial flow turbines operating with different organic fluids. The aim is to build general efficiency maps in accordance with the similarity principles for the performance prediction of turbines having very different design specifications (i.e., mass ow rate and enthalpy drop) and handling different working fluids. The so-called “size parameter” (SP) and the volumetric expansion ratio (VR) are identified as the best efficiency predictors for ORC turbines. The former is proportional to the turbine size and accounts for the scale effect, i.e. the detrimental effect on the performance when the machine is scaled down below a certain size; the latter accounts for the compressibility influence and, compared to the pressure expansion ratio, limits the influence of the fluid properties. Mean-line models are built for the preliminary design and performance estimation of radial and axial turbines in the Matlab ® environment implementing recent loss correlations to account for the flow irreversibilities and real fluid properties evaluated using the Refprop database. These models are used to simulate the turbine behavior and generate new design charts relating the efficiency to the design parameters (i.e., specific speed and velocity ratio for radial turbines; loading coefficient and flow coefficient for axial turbines). Several simulations are then carried out to generate the optimum designs for a wide range of design specifications and working fluids, and the associated efficiency maps in the SP-VR plane. These maps show that neither the size effect (SP), nor the compressibility effect (VR) have a negligible influence on the turbine performance: the efficiency increases as SP increases and VR decreases. Despite the general efficiency trends in the SP-VR maps are similar, differences due to the fluid effect exist. So, the critical temperature of the working fluid is proposed as third efficiency predictor and a general correlation between turbine efficiency and size parameter, volumetric flow ratio, critical temperature is obtained. The resulting generalized efficiency map is conceptually valid for any fluid and can be easily integrated into a comprehensive thermodynamic cycle optimization procedure to account for the real turbine performance and overcome the limitations due to a separate design of turbine and system.