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On the scaling of propagation of periodically generated vortex rings

Published online by Cambridge University Press:  22 August 2018

H. Asadi ,
H. Asgharzadeh  and
I. Borazjani Open the ORCID record for I. Borazjani [Opens in a new window]
H. Asadi
Affiliation:
Department of Mechanical Engineering, Texas A & M University, College Station, TX 77843, USA
H. Asgharzadeh
Affiliation:
Department of Mechanical and Aerospace Engineering, University at Buffalo, The State University of New York, Buffalo, NY 14260, USA
I. Borazjani*
Affiliation:
Department of Mechanical Engineering, Texas A & M University, College Station, TX 77843, USA
*
†Email address for correspondence: [email protected]
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Abstract

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.

JFM classification

Biological Fluid Dynamics: Biological Fluid Dynamics Vortex Flows: Vortex Flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 853 , 25 October 2018 , pp. 150 - 170
Copyright
© 2018 Cambridge University Press 

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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

Download Asadi et al. supplementary movie 1(Video)
Video 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

Download Asadi et al. supplementary movie 2(Video)
Video 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

Download Asadi et al. supplementary movie 3(Video)
Video 1 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

Download Asadi et al. supplementary movie 4(Video)
Video 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

Download Asadi et al. supplementary movie 5(Video)
Video 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

Download Asadi et al. supplementary movie 6(Video)
Video 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

Download Asadi et al. supplementary movie 7(Video)
Video 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

Download Asadi et al. supplementary movie 8(Video)
Video 3.3 MB