The key feature of the ORC technology is to exploit low-temperature heat sources with organic fluids which work in a thermodynamic state close to the saturation curve nd the critical region, where real gas effects are dominant. A a consequence, the proper description of the fluid behaviour in these conditions requires advanced thermodynamic models for which it is generally not possible to derive explicit relationshipts between different thermodynamic variables.

For cost and compactness reasons, ORC turbines often use a few, highly loaded, expansion stages that work in the supersonic regime. This is true in particular for small-scale ORC turbines for heat recovery from flow temperature sources. In this case, the expected Carnot efficiency of the ORC cycle is small and the isentropic efficiency of the turbine expander is a crucial parameter for the overall cycle efficiency. The development of advanced ORC turbine designs is then a key enabler for ORC machines with improved performance.

In this work, fast 2-D design methodology for supersonic ORC turbine stages with low degree of reaction is here proposed. Both the stator and rotor blade mean-lines are designed by means of the method of characteristics (MOC), extended to gases governed by general equations of state to take accurately into account dense-gas effects. In this case, it is not possible to find an analytical expression for the Pradtl-Meyer function and a numerical procedure is employed to integrate the characteristic equations. For supersonic rotor blade design the generalized MOC is combined to a free-vortex approach. Specifically, the MOC is used to design the blade portions that realizes the transition between the inlet uniform flow and a free-vortex flow, and the inverse. Since the actual blade design involves a finite thickness for the rotor leading edge, a bow shock is created upstream of the rotor. Assuming the rotor to be in a started condition (i.e. the relative flow is fully supersonic in the blade vane), the inlet flow angle and, subsequently, the stator stagger angle have to be chosen accordingly. An original algorithm is introduced to solve the unique incidence problem in the case of thermodynamically complex gases. Viscous effects have a considerable influence on the performance of nozzle guide vanes and rotor blades designed by using inviscid models. The effective nozzle-to-throat area of nozzle guide vanes is reduced by the development of the boundary layer. Similarly, the effective reaction degree of the rotor is modified. To prevent these unwanted effects, the blade designs resulting from the preceding inviscid model are corrected to account for the presence of turbulent boundary layers. An approximate calculation of the thickness of a compressible boundary layer subject to a generic pressure gradient is carried out by means of the Reshotko-Tucker method, adapted to gases governed by general thermophysical models. Finally, numerical simulations based on the RANS equations are carried out to investigate the performance of the turbine blade geometries. The results highlight the interest of the proposed methodology and in particular the importance of accounting for boundary layer effects at an early design stage.