2 results
Collisions of vortex rings with hemispheres
- T.H. New, Bowen Xu, Shengxian Shi
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- Journal:
- Journal of Fluid Mechanics / Volume 980 / 10 February 2024
- Published online by Cambridge University Press:
- 31 January 2024, A17
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- Article
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A numerical investigation was conducted on $Re_{\varGamma _{0}}=3000$ vortex rings colliding with wall-mounted hemispheres to study how their relative sizes affect the resulting vortex dynamics and structures. The hemisphere to vortex ring diameter ratio ranges from $D/d=0.5$ to $D/d=2$. Secondary/tertiary vortex rings are observed to result from hemispheric surface boundary layer separations rather than wall boundary layer separations as the diameter ratio increases. While those for $D/d\leq 1$ hemispheres can be attributed to sequential hemispheric and wall boundary layer separations, the primary vortex ring produces a series of secondary/tertiary vortex rings only along the $D/d=2$ hemispheric surface. This indicates that the presence of the wall makes little difference when the hemisphere is sufficiently large. On top of comparing vortex ring circulations and translational velocities between hemisphere and flat-wall based collisions, present collision outcomes have also been compared with those predicted by specific discharge velocity models. Additionally, comparisons of vortex core trajectories and vortex ring formation locations with earlier cylindrical convex surface based collisions provide more clarity on differences between two- and three-dimensional convex surfaces. Finally, vortex flow models are presented to account for the significantly different flow behaviour as the hemisphere size varies. Specifically, the vortex flow model for the $D/d=2$ hemisphere hypothesizes that the recurring tertiary vortex ring formations cease only when the primary vortex ring slows down sufficiently for the last tertiary vortex ring to entangle with it and render it incoherent. Until that happens, the primary vortex ring will continue to induce more tertiary vortex rings to form, with potential implications for heat/mass transfer optimizations.
Collision of vortex rings upon V-walls
- T. H. New, J. Long, B. Zang, Shengxian Shi
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- Journal:
- Journal of Fluid Mechanics / Volume 899 / 25 September 2020
- Published online by Cambridge University Press:
- 14 July 2020, A2
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A study on ${Re} =2000$ and 4000 vortex rings colliding with V-walls with included angles of $\theta =30^{\circ }$ to 120$^{\circ }$ has been conducted. Along the valley plane, higher Reynolds numbers and/or included angles of $\theta \leqslant 60^{\circ }$ lead to secondary/tertiary vortex-ring cores leapfrogging past the primary vortex-ring cores. The boundary layers upstream of the latter separate and the secondary/tertiary vortex-ring cores pair up with these wall-separated vortices to form small daisy-chained vortex dipoles. Along the orthogonal plane, primary vortex-ring cores grow bulbous and incoherent after collisions, especially as the included angle reduces. Secondary and tertiary vortex-ring core formations along this plane also lag those along the valley plane, indicating that they form by propagating from the wall surfaces to the orthogonal plane as the primary vortex ring gradually comes into contact with the entire V-wall. Circulation results show significant variations between the valley and orthogonal plane, and reinforce the notion that the collision behaviour for $\theta \leqslant 60^{\circ }$ is distinctively different from those at larger included angles. Vortex-core trajectories are compared to those for inclined-wall collisions, and secondary vortex-ring cores are found to initiate earlier for the V-walls, postulated to be a result of the opposing circumferential flows caused by the simultaneous collisions of both primary vortex-ring cores with the V-wall surfaces. These circumferential flows produce a bi-helical flow mode (Lim, Exp. Fluids, vol. 7, issue 7, 1989, pp. 453–463) that sees higher vortex compression levels along the orthogonal plane, which limit vortex stretching along the wall surfaces and produce secondary vortex rings earlier. Lastly, vortex structures and behaviour of the present collisions are compared to those associated with flat/inclined walls and round-cylinder-based collisions for a more systematic understanding of their differences.