Temporal and spatial evolution of vortex shedding for flow around a cylinder close to a wall

Abstract

Temporal and spatial vortex shedding evolution for flow around a circular cylinder near a plane boundary is investigated using three-dimensional direct numerical simulation, with a parameter space of boundary layer thickness-to-diameter δ/D = 0–1.4, gap-to-diameter G/D = 0.4 and Re = 350. For each δ/D, three consecutive wake stages are divided with time based on the dominated flow structures – mode A and mode B, of which spanwise wavelength is quantitatively measured by the autocorrelation function (ACF). In the first stage, mode A structures spread from two spanwise ends to the middle region and from upstream to downstream wake simultaneously. This stage is only dominated by ordered mode A structures and shows a weak three-dimensionality. In the second stage, mode B structures start to propagate in the same spanwise but opposite streamwise direction as mode A, and squeeze the mode A region until its disappearance. A mixture of mode A and mode B structures dominate the second stage and the flow is in the strongest three-dimensionality. In the third stage, the wake transits from a symmetric distribution of ordered mode B structure to an asymmetric distribution of disordered mode B structure, showing a relatively strong three-dimensionality. The typical vortex shedding patterns are analyzed by dynamic mode decomposition (DMD). When δ/D > 0, the dominant mode frequency (f0) of vortex shedding, larger than that of an isolated cylinder, decreases with the increase of δ/D. Due to suppression of the lower-surface vortex shedding, the flow structures with f0 are greatly reduced both in size and regularity with the increase of δ/D. Scattered mode components are reduced and the energy of each mode is more concentrated with increasing δ/D.