In recent years closed loop supercritical carbon dioxide Brayton cycles have drawn the attention of many researchers as they are characterized by a higher theoretic efficiency and smaller turbomachinery size compared to the conventional steam Rankine cycle for power generation. Currently, first prototypes of this emerging technology are under development and thus small scale sCO2 turbomachinery needs to be developed. However, the design of sCO2 turbines faces several new challenges, such as the very high rotational speed and the high power density. Thus, the eligibility of well-established radial inflow gas turbine design principles has to be reviewed regarding their suitability for sCO2 turbines. Therefore, this work reviews different suggestion for optimum velocity ratios for gas turbines and aims to re-establish it for sCO2 turbines. A mean line design procedure is developed to obtain the geometric dimensions for small scale sCO2 radial inflow turbines. By varying the specific speed and the velocity ratio, different turbine configurations are set up. They are compared numerically by means of CFD analysis to conclude on optimum design parameters with regard to maximum total-to-static efficiency. Six sets of simulations with different specific speeds between 0.15 and 0.52 are set up. Higher specific speeds could not be analyzed, as they require very high rotational speeds (more than 140k RPM) for small scale sCO2 turbines (up to 150kWe). For each set of simulations, the velocity ratio that effectuates maximum efficiency is identified and compared to the optimum parameters recommended for radial inflow turbines using subcritical air as the working fluid. It is found that the values for optimum velocity ratios suggested by Rohlik (1968) are rather far away from the optimum values indicated by the conducted simulations. However, the optimum values suggested by Aungier (2005), although also established for subcritical gas turbines, show an approximate agreement with the simulation results for sCO2 turbines. Though, this agreement should be studied for a wider range of specific speeds and a finer resolution of velocity ratios. Furthermore, for high specific speeds in combination with high velocity ratios, the pressure drop of the designed turbines is too high, so that the outlet pressure is beyond the critical point. For low specific speeds in combination with low velocity ratios, the power output of the designed turbines becomes very small. Geometrically, turbines with low specific speeds and high velocity ratios are characterized by very small blade heights, turbines with high specific speeds and small velocity ratios by very small diameters.
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