The linear stability of swirling vortex rings

C. Gargan-Shingles; M. Rudman; K. Ryan

doi:10.1063/1.4967732

Accurate numerical simulations of vortex flows II: Interaction of swirling vortex rings

Computers & Fluids ◽

10.1016/j.compfluid.2010.09.019 ◽

2011 ◽

Vol 41 (1) ◽

pp. 110-118 ◽

Cited By ~ 2

Author(s):

W. Kollmann

Keyword(s):

Numerical Simulations ◽

Vortex Rings ◽

Vortex Flows ◽

Swirling Vortex

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The Formation and Evolution of Turbulent Swirling Vortex Rings Generated by Axial Swirlers

Flow Turbulence and Combustion ◽

10.1007/s10494-019-00076-2 ◽

2019 ◽

Vol 104 (4) ◽

pp. 795-816 ◽

Cited By ~ 2

Author(s):

Chuangxin He ◽

Lian Gan ◽

Yingzheng Liu

Keyword(s):

Propagation Velocity ◽

Early Stage ◽

Axial Direction ◽

Vortex Rings ◽

Eddy Simulation ◽

Axis Parallel ◽

3D Printed ◽

Formation Number ◽

Formation And Evolution ◽

Swirling Vortex

AbstractThe present work investigates the formation process and early stage evolution of turbulent swirling vortex rings, by using planar Particle Image Velocimetry (PIV) and Large Eddy Simulation (LES). Vortex rings are produced in a piston-nozzle arrangement with swirl generated by 3D-printed axial swirlers in experiments. Idealised solid-body rotation is applied in LES to evaluate the effect of nozzle exit velocity profile in experiments. The Reynolds number (Re) based on the nozzle diameter D and the slug velocity U0 in the nozzle is 20,000. The swirl number S generated ranges from 0 (zero-swirl vortex ring) and 1.1, covering the two critical swirl numbers previously identified in a swirling jet. Both PIV and LES results show that the formation number F decreases linearly as S increases, with the maximum F ≈ 2.6 at S = 0 (produced by the swirler with straight vanes) and minimum F = 1.9 at S = 1.1. The corresponding maximum attainable circulation in the nozzle axis parallel plane also diminishes with increasing S. Evolution of compact rings produced by a stroke ratio L/D = 1.5 reveals that circulation decay rate is largely proportional to S. The trajectory of the vortex core in the axial direction, hence the ring axial propagation velocity, decreases as S, while that in the radial direction and the radial propagation velocity, increase with S. An empirical scaling function is proposed to scale these variables.

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Linear stability of inviscid vortex rings to axisymmetric perturbations

Journal of Fluid Mechanics ◽

10.1017/jfm.2019.473 ◽

2019 ◽

Vol 874 ◽

pp. 1115-1146

Author(s):

Bartosz Protas

Keyword(s):

Stability Analysis ◽

Linear Stability ◽

Equilibrium Configuration ◽

Three Dimensional ◽

Vortex Rings ◽

Meridional Plane ◽

The Family ◽

A Free Boundary Problem ◽

Shape Differentiation ◽

Axisymmetric Perturbations

We consider the linear stability to axisymmetric perturbations of the family of inviscid vortex rings discovered by Norbury (J. Fluid Mech., vol. 57, 1973, pp. 417–431). Since these vortex rings are obtained as solutions to a free-boundary problem, their stability analysis is performed using recently developed methods of shape differentiation applied to the contour-dynamics formulation of the problem in the three-dimensional axisymmetric geometry. This approach allows us to systematically account for the effects of boundary deformations on the linearized evolution of the vortex ring. We investigate the instantaneous amplification of perturbations assumed to have the same the circulation as the vortex rings in their equilibrium configuration. These stability properties are then determined by the spectrum of a singular integro-differential operator defined on the vortex boundary in the meridional plane. The resulting generalized eigenvalue problem is solved numerically with a spectrally accurate discretization. Our results reveal that while thin vortex rings remain neutrally stable to axisymmetric perturbations, they become linearly unstable to such perturbations when they are sufficiently ‘fat’. Analysis of the structure of the eigenmodes demonstrates that they approach the corresponding eigenmodes of Rankine’s vortex and Hill’s vortex in the thin-vortex and fat-vortex limit, respectively. This study is a stepping stone on the way towards a complete stability analysis of inviscid vortex rings with respect to general perturbations.

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