Low- and high-fidelity modeling of the flow in a multi-stage axial turbine for supercritical carbon dioxide power systems

Supercritical Carbon Dioxide (sCO₂) turbines, modeled on traditional axial-flow steam turbine design practices, often rely on empirical loss models developed by experimental campaigns on steam and gas turbines blades with aspect ratio greater than one. This study evaluates the applicability of these models for designing sCO₂ turbines featuring low aspect ratio blades (under 1). A low fidelity modeling tool (zTurbo), originally formulated based on Craig and Cox (CC) and Traupel (TR) loss correlations, was extended by integrating loss models proposed by Kacker Okappu (KO) and Aungier (AG). zTurbo was applied for Mean Line Design (MLD) of a five-stage axial-flow low aspect ratio sCO2 turbine (236.5 bar, 893.2 K inlet; 81 bar outlet). The four MLDs conceived using CC, KO, TR, AG loss models achieved flowpath total-to-total efficiency of 87.5%, 87.5%, 90.8%, and 91.9%. A detailed comparative analysis of four MLDs led to selection of AG loss model coupled with TR tip loss correlation to effectively capture all the losses within sCO2 turbine flowpath. zTurbo was linked with the Non-linear optimization algorithm to generate optimized AG based MLD flowpath exhibiting a total-to-total efficiency of 92.2 %. The optimized AG based MLD was then modeled to form full 3D flowpath, and high fidelity numerical simulations were performed to evaluate the turbine performance and losses encountered along the flowpath. Both modeling approaches showed strong agreement for estimating turbine flowpath total-to-total aerodynamic efficiency, differing by less than 0.1%. A detailed loss analysis comparison between two modeling techniques showed AG loss correlation reliability for estimating profile losses; however it overestimated the secondary losses, highlighting the need for detailed investigation into secondary flow development in sCO₂ turbines featuring low aspect ratio blades.