Windage loss model and flow characteristics for curved shroud gaps in a closed sCO₂ radial inflow turbine

A theoretical model for windage loss in curved shroud gaps under laminar flow conditions is developed by utilizing the concept of the arc differential method. An empirical model applicable to turbulent flow is established by incorporating rotational Reynolds number, throughflow Reynolds number, gap shapes, and wall thermal boundary conditions. The influence of these parameters on both flow characteristics and windage loss is systematically analyzed in this paper. The findings reveal that the skin friction coefficient decreases with higher rotational Reynolds numbers but increases with elevated throughflow Reynolds numbers, with a distinct transition from plunge zone to a plateau zone observed at a rotational Reynolds number of 6.8 × 10⁶. While increased throughflow Reynolds numbers enhance wall shear stress, thereby improving momentum transfer efficiency within the boundary layer. The dominance of the strain tensor over the rotation tensor within the wall boundary layer directly translates to frictional resistance. And flow separation vortices are identified near the inlet. Larger radius ratios amplify windage loss, particularly in midstream and downstream regions characterized by high shear stress and turbulent kinetic energy. Elevated rotor wall temperatures reduce the skin friction coefficient due to altered local fluid temperature distributions compared to adiabatic conditions. The proposed models address the current research gap in predicting windage loss for curved gaps and provide critical insights for optimizing sCO₂ radial inflow turbine designs.