Theoretical Estimation of Minimum and Maximum Allowable Rotational Speed of Supercritical CO₂ Inward Flow Radial Turbine

Supercritical CO₂ inward flow radial turbines necessitate high operating speeds due to the high density of sCO₂, especially in sub-MW scale power generation where rotational speeds can be in the range of 50k to 150k rpm. Although designing the turbine at these high rotational speeds is reasonable from the aerodynamic efficiency point of view but generally not practical to operate. A theoretical framework based on 1-D meanline analysis is built to evaluate the minimum and maximum rotational speed limits corresponding to a set of boundary conditions and operating constraints. The results show that minimum allowable speed depends on the inlet velocity triangle (IVT) and is constrained by inlet Mach number, inlet blade height, and inlet flow angle. On the other hand, maximum allowable speed depends on the outlet velocity triangle (OVT) and is constrained by outlet relative Mach number, outlet hub radius, and blade speed. The theoretical models are demonstrated from kilowatt to megawatt power levels, and the results are compared with commercial software and Balje’s Ns-Ds diagram. Although this study is highlighted in the context of supercritical CO₂ as the working fluid, in principle, the same models are equally valid for any working fluid.