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On the scaling of propagation of periodically generated vortex rings

  • H. Asadi (a1), H. Asgharzadeh (a2) and I. Borazjani (a1)


The propagation of periodically generated vortex rings (period $T$ ) is numerically investigated by imposing pulsed jets of velocity $U_{jet}$ and duration $T_{s}$ (no flow between pulses) at the inlet of a cylinder of diameter $D$ exiting into a tank. Because of the step-like nature of pulsed jet waveforms, the average jet velocity during a cycle is $U_{ave}=U_{jet}T_{s}/T$ . By using $U_{ave}$ in the definition of the Reynolds number ( $Re=U_{ave}D/\unicode[STIX]{x1D708}$ , $\unicode[STIX]{x1D708}$ : kinematic viscosity of fluid) and non-dimensional period ( $T^{\ast }=TU_{ave}/D=T_{s}U_{jet}/D$ , i.e. equivalent to formation time), then based on the results, the vortex ring velocity $U_{v}/U_{jet}$ becomes approximately independent of the stroke ratio $T_{s}/T$ . The results also show that $U_{v}/U_{jet}$ increases by reducing $Re$ or increasing $T^{\ast }$ (more sensitive to $T^{\ast }$ ) according to a power law of the form $U_{v}/U_{jet}=0.27T^{\ast 1.31Re^{-0.2}}$ . An empirical relation, therefore, for the location of vortex ring core centres ( $S$ ) over time ( $t$ ) is proposed ( $S/D=0.27T^{\ast 1+1.31Re^{-0.2}}t/T_{s}$ ), which collapses (scales) not only our results but also the results of experiments for non-periodic rings. This might be due to the fact that the quasi-steady vortex ring velocity was found to have a maximum of 15 % difference with the initial (isolated) one. Visualizing the rings during the periodic state shows that at low $T^{\ast }\leqslant 2$ and high $Re\geqslant 1400$ here, the stopping vortices become unstable and form hairpin vortices around the leading ones. However, by increasing $T^{\ast }$ or decreasing $Re$ the stopping vortices remain circular. Furthermore, rings with short $T^{\ast }=1$ show vortex pairing after approximately one period in the downstream, but higher $T^{\ast }\geqslant 2$ generates a train of vortices in the quasi-steady state.


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Type Description Title

Asadi et al. supplementary movie 1
The isosurface of vorticity magnitude colored by helicity starting from rest (t=0) to quasi-steady state for case 3 (Re=1400, T*=1). Link in the text: Movie 1

 Video (26.9 MB)
26.9 MB

Asadi et al. supplementary movie 2
Out-of-plane vorticity for case 3 (Re=1400, T*=1) contours starting from rest (t=0) to quasi-steady state. Link in the text: Movie 2

 Video (4.2 MB)
4.2 MB

Asadi et al. supplementary movie 3
Out-of-plane vorticity on the midplane for case 3 (Re=1400, T*=1) contours during quasi-steady state. Link in the text: Movie 3

 Video (1.0 MB)
1.0 MB

Asadi et al. supplementary movie 4
Out-of-plane vorticity on the midplane for case 4 (Re=1400, T*=2) contours during quasi-steady state. Link in the text: Movie 4

 Video (2.7 MB)
2.7 MB

Asadi et al. supplementary movie 5
Out-of-plane vorticity on the midplane for case 5 (Re=11,500, T*=1) contours during quasi-steady state. Link in the text: Movie 5

 Video (5.5 MB)
5.5 MB

Asadi et al. supplementary movie 6
Out-of-plane vorticity on the midplane for case 6 (Re=11,500, T*=2) contours during quasi-steady state. Link in the text: Movie 6

 Video (3.9 MB)
3.9 MB

Asadi et al. supplementary movie 7
The isosurface of Q-criteria for case 6 (Re=11,500, T*=2) from rest (t=0) to quasi-steady state. Link in the text: Movie 7

 Video (4.7 MB)
4.7 MB

Asadi et al. supplementary movie 8
The isosurface of Q-criteria for case 5 (Re=11,500, T*=1) from rest (t=0) to quasi-steady state. Link in the text: Movie 8

 Video (3.3 MB)
3.3 MB


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