The stator vanes of high-temperature organic Rankine cycle (ORC) radial-inflow turbines (RIT) operate under severe expansion ratios and the associated fluid-dynamic losses account for nearly two-thirds of the total losses generated within the blading passages. The efficiency of the machine can strongly benefit from specialized high-fidelity design methods able to provide shapes attenuating shock wave formation, consequently reducing entropy generation across the shock-wave and mitigating shock-wave boundary layer interaction. Shape optimization is certainly a viable option to deal with supersonic ORC stator design, but it is computationally expensive. In this work, a robust method to approach the problem at reduced computational cost is documented. The method consists of a procedure encompassing the method of characteristics (MoC), extended to nonideal fluid flow, for profiling the diverging part of the nozzle. The subsonic section and semibladed suction side are retrieved using a simple conformal geometrical transformation. The method is applied to design a supersonic ORC stator working with Toluene vapor, for which two blade shapes were already available. The comparison of fluid-dynamic performance clearly indicates that the MoC-Based method is able to provide the best results with the lowest computational effort, and is therefore suitable to be used in a systematic manner for drawing general design guidelines.

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