A numerical study of a vortex ring impacting a permeable wall

Abstract

In this paper, we numerically simulate a vortex ring impacting a permeable wall by using a lattice Boltzmann method. The study is motivated by recent publications on vortex ring/permeable wall interaction and our desire to address some of the unanswered questions such as evolution of core vorticity, kinetic energy, and enstrophy of the flow field during the interaction. The simulation was conducted for a wide range of parameters, namely, wall open-area ratios (ϕ) (0 ≤ ϕ ≤ 1), wire structure dimensions (A) (0.015 ≤ A ≤ 0.1), wall-thicknesses (H) (0.015 ≤ H ≤ 1), and Reynolds numbers (\documentclass[12pt]{minimal}\begin{document}$Re_\Gamma$\end{document}ReΓ) (\documentclass[12pt]{minimal}\begin{document}$500 \le Re_\Gamma \le 5000$\end{document}500≤ReΓ≤5000). Results show that the flow characteristics upstream and downstream of the permeable wall depends on these parameters. Specifically, increasing ϕ or \documentclass[12pt]{minimal}\begin{document}$Re_\Gamma$\end{document}ReΓ enhances vorticity transport across the permeable wall, leading to a regenerated vortex ring, while increasing H impedes vorticity transportation and the formation of regenerated vortex ring. Moreover, larger A promotes vortex shedding from wire grids and generates fine-scale flow structures in the wake region. The study further shows a strong correlation between the attainment of maximum enstrophy and the lifting of the secondary vortex ring from the wall by the induced velocity of the primary vortex ring. While increasing ϕ causes the peak enstrophy to decrease in the upstream region and increase in the downstream region, increasing wall thickness has the opposite effect on the peak enstrophy. On the other hand, increasing wire dimension reduces peak enstrophy in both the upstream and downstream regions, while increasing Reynolds number has the opposite effect on the peak enstrophy.

Instabilities of interacting vortex rings generated by an oscillating disk

“…It has been observed that the presence of a permeable wall leads to significant changes in the flow field, and the final outcome of the interaction is itself strongly influenced by surface permeability. Indeed, under certain favourable conditions, the primary vortex ring was observed to pass through the permeable wall and continue as a modified vortex ring in its lee [20]. A vortex ring can also interact with another one, as can be observed in the head-on collision of two vortex rings.…”

“…The second, and richer, category of vortex ring instability consists of coupled instabilities associated with the primary vortex ring undergoing an interaction, for example with another ring [17] or with a boundary such as a wall [18][19][20]. Such coupled instabilities are typically more complicated than the more studied isolated instabilities.…”

Leapfrogging of multiple coaxial viscous vortex rings

“…23 The code has been extensively validated for several benchmark problems involving the motion of a vortex ring in viscous liquid. [18][19][20] Interested readers are referred to Refs. 18-20 for the implementation details.…”

“…As far as we are aware, this has not been carried out previously. To study the motion of multiple coaxial viscous vortex rings, the lattice Boltzmann method (LBM), which has been previously verified and applied to vortex dynamics, [18][19][20] is used to simulate the motion of multiple viscous rings.…”

Quantitative visualization of vortex ring structure during wall impingement subject to background rotation

“…Yamada et al (1982) and Walker et al (1987) experimentally observed fingering of vortex ring after the impingement. Interaction with other type of solid objects was reported by Naaktgeboren et al (2012), Cheng et al (2014), andMujal-Colilles et al (2015) for permeable plates. Suzuki and Kumagai et al (2007), Masuda et al (2012), Bethke et al (2012), and Misaka (2012) studied particulate layers transported by a vortex ring.…”