Laminar separation bubble on a rotating cylinder in uniform flow

Abstract

We study the effect of spin ( 0 ≤ α ≤ 2) of a cylinder, placed in uniform flow, on the transition of the boundary layer. Large Eddy Simulation, with the Sigma turbulence model to account for the sub-grid scales, is carried out using a stabilized finite element formulation. The Reynolds numbers ( R e = 0.6 × 10 5 and 1.0 × 10 5) lie in the high-subcritical regime for a non-rotating cylinder where the boundary layer separates in a laminar state and does not reattach. Magnus effect is observed at low α wherein separation is delayed on the retreating side and preponed on the advancing side, resulting in a lift force that increases with increase in α. At a certain critical α, the boundary layer on the advancing side transitions to a turbulent state, causing it to reattach. A laminar separation bubble (LSB) forms, significantly delaying the final separation and increasing suction. At R e = 1.0 × 10 5, this suction overcomes that on the retreating side, leading to a reversal in the direction of lift force, referred to as the inverse Magnus effect. The LSB is accompanied by weakened vortex shedding at increased frequency. The spatial extent of the LSB and the magnitude of reverse lift, at a given Re, decreases with increase in α. The lift force changes direction yet again at a certain α marking the end of the inverse Magnus effect regime and beginning of the second Magnus effect regime. The LSB vanishes beyond a certain spin rate, and the boundary layer directly transitions to a turbulent state.