Free-surface deformation and air entrainment in turbulent flow past a rotating cylinder beneath a water–air interface

The flow past a fully submerged rotating cylinder beneath a free surface involves complex multiphase interactions, including free-surface deformation, air entrainment, and wave breaking. Using large-eddy simulation coupled with the volume-of-fluid method, we investigate these phenomena at R e = 6 × 10 4 and spin ratio α = 2 over a range of submergence depths H / D = 3 –100, Froude numbers F r = 2.0 –3.2, and both clockwise and anticlockwise rotations. The free surface exhibits markedly different responses depending on the rotation direction: clockwise rotation produces a deep wave trough accompanied by intense air entrainment, whereas anticlockwise rotation generates a wave crest with substantially less entrainment. The two-phase mixing region volume is quantified and found to exhibit local extrema, reflecting the shifting balance between gravity- and inertia-dominated regimes for the parameter set investigated. The lift coefficient exhibits a significant reduction that is strongly correlated with the occurrence of intense air entrainment, with an optimal submergence of H / D = 5 providing maximum lift under moderate Froude numbers. The streamwise velocity field reveals how air entrainment alters the wake structure and promotes energy dissipation. These findings provide a fundamental quantitative understanding of multiphase Magnus-effect flows.