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Direct numerical and large-eddy simulation of trefoil knotted vortices

Published online by Cambridge University Press:  15 January 2021

Xinran Zhao Open the ORCID record for Xinran Zhao [Opens in a new window] ,
Zongxin Yu Open the ORCID record for Zongxin Yu [Opens in a new window] ,
Jean-Baptiste Chapelier Open the ORCID record for Jean-Baptiste Chapelier [Opens in a new window]  and
Carlo Scalo Open the ORCID record for Carlo Scalo [Opens in a new window]
Xinran Zhao
Affiliation:
School of Mechanical Engineering, Purdue University, IN 47907, USA
Zongxin Yu
Affiliation:
School of Mechanical Engineering, Purdue University, IN 47907, USA
Jean-Baptiste Chapelier
Affiliation:
School of Mechanical Engineering, Purdue University, IN 47907, USA
Carlo Scalo*
Affiliation:
School of Mechanical Engineering, Purdue University, IN 47907, USA
*
†Email address for correspondence: [email protected]
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Abstract

This paper investigates pre- and post-reconnection dynamics of an unperturbed trefoil knotted vortex for circulation-based Reynolds numbers $Re_\varGamma = 2\times 10^3$ and $6\times 10^3$ by means of direct numerical simulations based on an adaptive mesh refinement framework. Companion coherent-vorticity preserving large-eddy simulations are also carried out on a uniform Cartesian grid. The complete vortex structure and flow evolution are simulated, including reconnection and subsequent separation into a smaller and a larger vortex ring, and the resulting helicity dynamics. The self-advection velocity before reconnection is found to scale with inviscid parameters. The reconnection process, however, occurs earlier (and more rapidly) in the higher Reynolds number case due to higher induced velocities associated with a thinner vortex core. The vortex propagation velocities after reconnection and separation are also affected by viscous effects, more prominently for the smaller vortex ring; the larger one is shown to carry the bulk of the helicity and enstrophy after reconnection. The domain integrated, or total helicity, $H(t)$, does not significantly change up until reconnection, at which point it varies abruptly due to the rapid dissipation of helicity caused by super-helicity hotspots localized at the reconnection sites. The total helicity dissipation rate predicted by the large-eddy simulation agrees reasonably well with the direct numerical simulation results, with a significant contribution from the modelled subgrid-scale stresses. On the other hand, variations in the vortex centreline helicity, $H_C(t)$, and the vortex-tube-integrated helicity $H_V(t)$ are less sensitive to the reconnection process. Periodic vortex bursting events are also observed and are shown to be due to converging axial flow velocities in the detached vortex rings at later stages of evolution.

JFM classification

Vortex Flows: Vortex dynamics Turbulent Flows: Turbulence simulation Vortex Flows: Vortex interactions
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 910 , 10 March 2021 , A31
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

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