On the unsteady wake flow behind a sphere with large transverse-rotating speeds

Abstract

The unsteady wake downstream of a spinning sphere with a Reynolds number of 7930 (Re=UoD/ν, based on the sphere diameter and the free-stream velocity) and a range of spinning ratios (the ratio between the surface velocity and free-stream velocity, α=Vs/Uo) from 0 to 6.0 were studied using time-resolved particle image velocimetry. The Reynolds stresses and proper orthogonal decomposition results indicated that the wake exhibited distinct features in different spinning ratio regimes, and the state of the boundary layer played an important role in forming these features. In regime I (α≤0.25) where the boundary layer around the sphere was laminar, a pair of counter-rotating vortices emerged in the wake with unsteady size and position. The bottom boundary layer transitioned from laminar to turbulent as α increased from 0.25 to 0.75 (regime II). The transition caused a significant increase in the stream-wise stress as the unsteadiness becomes more coherent. The sphere was gradually covered by the turbulent boundary layer as α increased in regimes III and IV (0.75<α≤3.0). A large separation bubble was created in cases with α>3.0 (regime V); flow structures with a large stream-wise momentum separated from the bubble and was shed downstream with a strong flapping motion in the vertical direction, leading to large vertical stress behind the sphere.