Windage and Leakage Losses in Impeller Back Gap and Labyrinth Seal Cavities of Supercritical CO₂ Centrifugal Compressors

The windage loss in impeller back gap and labyrinth seal cavities significantly impacts the aerodynamic performances of supercritical carbon dioxide (sCO₂) compressors. To accurately calculate windage loss, essential factors affecting the skin friction coefficients C_f,d (disk-type gap) and C_f,s (shaft-type gap), including Reynolds number Re, pressure ratio π, and radius ratio η, are investigated in this paper. The flow characteristics of the gap are analyzed and prediction models are proposed. The results indicate that both C_f,d and C_f,s decrease with increasing Re and grow with π and η, attributable to expanded high-vorticity regions caused by enhanced flow instability and larger vortices. The leakage flow rate m is unchanged for Re < 10⁶ since the fluid can flow into the impeller back gap, and slightly decreases for Re ≥ 10⁶ due to the centrifugal force and the inhibition effect of the vortices filling inlet regions. Moreover, the m grows with π and η due to a larger pressure difference and through-flow area. Maximal relative deviations of 6.23% and 6.83% can satisfy the requirements for calculating accurate windage loss in the impeller back gap and labyrinth seal cavities, which help the primary design of sCO₂ compressors.