Discrete shedding of secondary vortices along a modified Kaden spiral

TL;DR

This study investigates the formation, shedding, and trajectories of secondary vortices along a modified Kaden spiral in fluid flow around a rotating plate, revealing how vortex shedding timing depends on Reynolds number and circulation dynamics.

Contribution

It demonstrates that the shear layer roll-up, primary vortex trajectory, and secondary vortex paths can be predicted by a modified Kaden spiral, and analyzes the timing of vortex shedding.

Findings

Secondary vortices are discretely shed at Re>4000.

Shedding interval increases with decreasing Reynolds number.

Shedding timing correlates with circulation feeding rate.

Abstract

When an object is accelerated in a fluid, a primary vortex is formed through the roll-up of a shear layer. This primary vortex does not grow indefinitely and will reach a limiting size and strength. Additional vorticity beyond the critical limit will end up in a trailing shear layer and accumulate into secondary vortices. The secondary vortices are typically considerably smaller than the primary vortex. Here, we focus on the formation, shedding, and trajectory of secondary vortices generated by a rotating rectangular plate in a quiescent fluid using time-resolved particle image velocimetry. The Reynolds number (Re) is varied from 840 to 11150. At low Re, the shear layer is a continuous uninterrupted layer of vorticity that rolls up into a single coherent primary vortex. At Re=1955, the shear layer becomes unstable. For Re>4000, secondary vortices are discretely released from the plate tip. First, we demonstrate that the roll-up of the shear layer, the trajectory of the primary vortex, and the path of secondary vortices can be predicted by a modified Kaden spiral. Second, the timing of the secondary vortex shedding is analysed. The time interval between the release of successive secondary vortices is not constant during the rotation but increases the more vortices have been shed. The shedding time interval also increases with decreasing Reynolds number. The increased time interval under both conditions is due to a reduced circulation feeding rate.