Model improvement for shaft-type windage loss with CO₂

To improve the prediction accuracy of skin friction coefficient C_f related shaft-type windage loss in generators of turbine-alternator-compressor (TAC) units, an original model is validated, the flow characteristics are analyzed, and an improved model is proposed. It indicates that the C_f decreases with Reynolds number Re increasing and grows as radius ratio η rises. The results reveal that the original model isn't applicable to predict C_f due to the lack of models at Re = 10² ∼ 5 × 10² and large deviations at 7 × 10³ ≤ Re ≤ 3 × 10⁴ and Re > 3 × 10⁴. The flow field implies that Re = 10² is regarded as a critical point between laminar flow and turbulence. The maximal deviation of 9 % confirms that the improved model is reliable at Re = 10 ∼ 10⁷. The conclusions help predict shaft-type windage loss accurately in generators of TAC units, which is beneficial for designing smaller sCO₂ power devices.