&nbsp; &nbsp; &nbsp; Literature shows an inward flow radial turbine with supercritical CO2 as the working fluid operates at a high rotational speed. The requirement of high rotational speed is severe in small-scale power generation units with high specific power output, where rotational speed can be in the range of 60,000 to 120,000 RPM. Although designing the turbine at these high rotational speeds is reasonable from an efficiency point of view but sometimes not practical to operate. Then, a lower design speed with compromises in the aerodynamic efficiency is a more practical choice. However, the choice of design point rotational speed significantly influences turbine geometry (Diameter, blade height, metal angles, etc.) and the flow physics (Flow angles, blade loading, Mach number, etc.) inside. The practical feasibility of turbine geometry and flow physics put constraints on the minimum and maximum possible design point shaft speed. A typical preliminary design process that uses empirical correlations such as Ns-Ds diagrams to select shaft speed does not provide insights to evaluate rotational speed limits.&nbsp; &nbsp; &nbsp; &nbsp;This study builds a theoretical framework based on one-dimensional meanline analysis to evaluate the minimum and maximum possible shaft rotational speed fulfilling all boundary conditions and practical constraints. The study shows that minimum allowable speed depends on the inlet velocity triangle 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, velocity distribution, shaft diameter, and hub-to-shroud diameter ratio and constrained by outlet relative Mach number and material strength. Inclusion of material and manufacturing limitations such as minimum blade height, minimum shaft diameter, and flow limitations such as maximum allowable Mach number makes a robust preliminary design. The analysis is demonstrated in the context of supercritical CO2 radial turbines ranging from kilowatt to megawatt power levels, and the results are compared with industry-standard commercial software Axstream®. Case studies show a good agreement with both the commercial software and the Ns-Ds diagram. Although this study is highlighted in the context of supercritical CO2 as the working fluid, in principle, the same analysis is equally valid for any working fluid.

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

Paper Proceedings: https://asmedigitalcollection.asme.org/GTINDIA/GTINDIA2021/volume/85536

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