Numerical study of gas-liquid flow in a rotating hollow shaft under vacuum conditions

Gas–liquid two-phase flow inside a rotating hollow shaft under vacuum conditions is critical to internal cooling of high-speed flywheel systems, yet its coupled flow and energy-loss mechanisms remain unclear. Numerical simulations are performed to investigate the effects of axial through-flow and shaft rotation on phase distribution, velocity structure, hydrodynamic torque, and pressure loss. The results show that liquid distribution is governed by the balance between centrifugal confinement and axial transport. At low rotational intensity, centrifugal stratification enhances liquid accumulation, whereas beyond approximately 2000 rpm, liquid content becomes primarily controlled by inlet velocity. Rotation fundamentally reorganizes the velocity field, leading to the formation of a quasi-fully developed near-wall rotating liquid film. Hydrodynamic torque and pressure loss are highly localized, originating mainly from circumferential shear near the inner cylindrical wall and the top impingement region. When rotational speed and axial flow rate are properly matched, rotational energy stabilizes near-wall flow and pressure loss increases smoothly; otherwise, excessive rotation leads to enhanced shear dissipation and less favorable mean flow organization, resulting in disproportionately larger torque and pressure losses. These findings provide a hydrodynamic basis for the design of internal cooling strategies in vacuum-operated flywheel systems by clarifying liquid coverage, mechanical loss, and pressure-loss mechanisms.