Large-eddy simulation of flow over a rotating cylinder: the lift crisis at

Abstract

We present wall-resolved large-eddy simulation (LES) of flow with free-stream velocity $\boldsymbol{U}_{\infty }$ over a cylinder of diameter $D$ rotating at constant angular velocity $\unicode[STIX]{x1D6FA}$ , with the focus on the lift crisis, which takes place at relatively high Reynolds number $Re_{D}=U_{\infty }D/\unicode[STIX]{x1D708}$ , where $\unicode[STIX]{x1D708}$ is the kinematic viscosity of the fluid. Two sets of LES are performed within the ( $Re_{D}$ , $\unicode[STIX]{x1D6FC}$ )-plane with $\unicode[STIX]{x1D6FC}=\unicode[STIX]{x1D6FA}D/(2U_{\infty })$ the dimensionless cylinder rotation speed. One set, at $Re_{D}=5000$ , is used as a reference flow and does not exhibit a lift crisis. Our main LES varies $\unicode[STIX]{x1D6FC}$ in $0\leqslant \unicode[STIX]{x1D6FC}\leqslant 2.0$ at fixed $Re_{D}=6\times 10^{4}$ . For $\unicode[STIX]{x1D6FC}$ in the range $\unicode[STIX]{x1D6FC}=0.48{-}0.6$ we find a lift crisis. This range is in agreement with experiment although the LES shows a deeper local minimum in the lift coefficient than the measured value. Diagnostics that include instantaneous surface portraits of the surface skin-friction vector field $\boldsymbol{C}_{\boldsymbol{f}}$ , spanwise-averaged flow-streamline plots, and a statistical analysis of local, near-surface flow reversal show that, on the leeward-bottom cylinder surface, the flow experiences large-scale reorganization as $\unicode[STIX]{x1D6FC}$ increases through the lift crisis. At $\unicode[STIX]{x1D6FC}=0.48$ the primary-flow features comprise a shear layer separating from that side of the cylinder that moves with the free stream and a pattern of oscillatory but largely attached flow zones surrounded by scattered patches of local flow separation/reattachment on the lee and underside of the cylinder surface. Large-scale, unsteady vortex shedding is observed. At $\unicode[STIX]{x1D6FC}=0.6$ the flow has transitioned to a more ordered state where the small-scale separation/reattachment cells concentrate into a relatively narrow zone with largely attached flow elsewhere. This induces a low-pressure region which produces a sudden decrease in lift and hence the lift crisis. Through this process, the boundary layer does not show classical turbulence behaviour. As $\unicode[STIX]{x1D6FC}$ is further increased at constant $Re_{D}$ , the localized separation zone dissipates with corresponding attached flow on most of the cylinder surface. The lift coefficient then resumes its increasing trend. A logarithmic region is found within the boundary layer at $\unicode[STIX]{x1D6FC}=1.0$ .