Discrete shedding of secondary vortices along a modified Kaden spiral. (30th April 2021)

• Record Type: Journal Article
• Authors: Francescangeli, Diego; Mulleners, Karen
• Is Part Of: Journal of fluid mechanics. Volume 917(2021)
• Publication Date: 2021-04-30
• Subjects: vortex shedding; Fluid mechanics -- Periodicals; 532.005
• DOI: 10.1017/jfm.2021.259
• Languages: English
• ISSNs: 0022-1120

Abstract

Abstract: 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. In this paper, 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 $\textit {Re}$ based on the maximum rotational velocity of the plate and the distance between the centre of rotation and the tip of the plate is varied from 840 to 11 150. At low $\textit {Re}$, the shear layer is a continuous uninterrupted layer of vorticity that rolls up into a single coherent primary vortex. At $\textit {Re} = 1955$, the shear layer becomes unstable and secondary vortices emerge and subsequently move away from the tip of the plate. For $\textit {Re} > 4000$, secondary vortices are discretely released from the plate tip and are not generated from the stretching of an unstable shear layer. 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 for the entire $\textit {Re}$ range considered. Second, the timing of the secondary vortex shedding is analysed using the swirling strength criterion. The separation time of each secondary vortex is identified as a local maximum in the temporal evolution of the average swirling strength close to the plate tip. 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.