Computational aspects of three-dimensional Vortex Element Methods: Applications with vortex rings

Accurate numerical simulations of vortex rings impinging on flat boundaries revealed the same features observed in experiments. The results for the impact with a free-slip wall compared very well with previous numerical simulations that used spectral methods, and were also in qualitative agreement with experiments. The present simulation is mainly devoted to studying the more realistic case of rings interacting with a no-slip wall, experimentally studied by Walker et al. (1987). All the Reynolds numbers studied showed a very good agreement between experiments and simulations, and, at Rev > 1000 the ejection of a new ring from the wall was seen. Axisymmetric simulations demonstrated that vortex pairing is the physical mechanism producing the ejection of the new ring. Three-dimensional simulations were also performed to investigate the effects of azimuthal instabilities. These simulations have confirmed that high-wavenumber instabilities originate in the compression phase of the secondary ring within the primary one. The large instability of the secondary ring has been explained by analysis of the rate-of-strain tensor and vorticity alignment. The differences between passive scalars and the vorticity field have been also investigated.

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Application of a Vortex Method to Fluid Dynamics in Sports Science

Volume 1: Symposia, Parts A and B ◽

10.1115/fedsm2007-37066 ◽

2007 ◽

Cited By ~ 1

Author(s):

Kyoji Kamemoto ◽

Akira Ojima

Keyword(s):

Fluid Dynamics ◽

Three Dimensional ◽

Vortex Method ◽

Mathematical Treatment ◽

Sports Science ◽

Lagrangian Simulation ◽

Eddy Simulation ◽

Flow Features ◽

Vortex Element ◽

Basic Equations

This paper describes a pioneering work of practical application of an advanced vortex method in the field of fluid dynamics in sports science. The vortex method developed by the present authors is one of vortex element methods based on the Biot-Savart law, and it is known that the method provides a Lagrangian simulation of unsteady and vortical flows. In this study, in order to examine the applicability of the vortex method, three-dimensional, complex and unsteady flows around an isolated 100 m runner and a ski-jumper were calculated. Basic equations and mathematical treatment of the method are explained in this paper, and calculation conditions and panel data of deforming configuration of the athletes are described. As results of the present study, vortical and unsteady flow features around a runner and a ski-jumper are understood, and unsteady variation of aerodynamic forces corresponding to deformation of body configuration due to athletic motion are calculated. And, it is confirmed that the advanced vortex element method is a promising way to a grid-free Lagrangian large eddy simulation of unsteady and complex flows around dynamic bodies of athletes.

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Curvature-induced deformations of the vortex rings generated at the exit of a rectangular duct

Journal of Fluid Mechanics ◽

10.1017/jfm.2018.988 ◽

2019 ◽

Vol 864 ◽

pp. 141-180 ◽

Cited By ~ 2

Author(s):

Abbas Ghasemi ◽

Burak Ahmet Tuna ◽

Xianguo Li

Keyword(s):

Cross Section ◽

Rectangular Cross Section ◽

Three Dimensional ◽

Single Mode ◽

The Self ◽

Vortex Rings ◽

Potential Core ◽

Vortex Pairing ◽

Time Space ◽

Axis Switching

Rectangular air jets of aspect ratio $2$ are studied at $Re=UD_{h}/\unicode[STIX]{x1D708}=17\,750$ using particle image velocimetry and hot-wire anemometry as they develop naturally or under acoustic forcing. The velocity spectra and the spatial theory of linear stability characterize the fundamental ($f_{n}$) and subharmonic ($f_{n}/2$) modes corresponding to the Kelvin–Helmholtz roll-up and vortex pairing, respectively. The rectangular cross-section of the jet deforms into elliptic/circular shapes downstream due to axis switching. Despite the apparent rotation of the vortex rings or the jet cross-section, the axis-switching phenomenon occurs due to reshaping into rounder geometries. By enhancing the vortex pairing, excitation at $f_{n}/2$ shortens the potential core, increases the jet spread rate and eliminates the overshoot typically observed in the centreline velocity fluctuations. Unlike circular jets, the skewness and kurtosis of the rectangular jets demonstrate elevated anisotropy/intermittency levels before the end of the potential core. The axis-switching location is found to be variable by the acoustic control of the relative expansion/contraction rates of the shear layers in the top (longer edge), side (shorter edge) and diagonal views. The self-induced vortex deformations are demonstrated by the spatio-temporal evolution of the phase-locked three-dimensional ring structures. The curvature-induced velocities are found to reshape the vortex ring by imposing nonlinear azimuthal perturbations occurring at shorter wavelengths with time/space evolution. Eventually, the multiple high-curvature/high-velocity regions merge into a single mode distribution. In the plane of the top view, the self-induced velocity distribution evolves symmetrically while the tilted ring results in the asymmetry of the azimuthal perturbations in the side view as the side closer to the acoustic source rolls up in more upstream locations.

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