Model of skin friction coefficient in a supercritical CO₂ turbine-alternator-compressor unit

To accurately predict shaft-type and disk-type windage losses in gaps of supercritical CO₂ (sCO₂) turbine-alternator-compressor (TAC) units, the factors influencing skin friction coefficients C_f,s and C_f,d are investigated, the flow characteristics are analyzed, and the models of C_f,s and C_f,d are proposed. The results reveal the C_f,s and C_f,d decrease with Reynolds number Re increasing, but rise as pressure ratio π and radius ratio η. The leakage flow rate remains constant for Re < 10⁵ and decreases when Re ≥ 10⁵ as Re increases, but grows with π and η. Furthermore, the influences of Re on flow are minor compared to π, and vorticity growth with η increases flow instability, which makes corresponding C_f,s and C_f,d grow. The maximal relative deviations of 5.24% and 4.87% prove the proposed models are reliable. These conclusions accurately predict windage loss in whole gaps of TAC units, which helps design small sCO₂ power devices.