Numerical simulation and flow-visualization experiment on deformation of pseudo-elliptic vortex rings

Abstract

The deformation of a pseudo-elliptic vortex ring with circulation F was studied by a three-dimensional vortex blob method which included the viscous diffusion of vorticity. The circumference of this vortex ring consisted of two parallel line segments of the same length connected by two semicircles of the same radius R, the length of the major axis being denoted by L. The cross section of the vortex ring was represented by multiple vortex blobs with overlapping cores, while the circumference of the vortex ring was divided into a number of such sections. Numerical calculations were performed for the aspect ratios L /2R ~" 2.0-12,0, the initial core radius LT cs = 0.20R, and Reynolds number F /v c~1500, v being the kinematic viscosity. The vurtex rings yielded four fundamental patterns of deformation which included the axis switching and the split, depending on the aspect ratio, A flow-visualization experiment confirmed three of the four fundamental patterns, and was in sufficient agreement with the computation for the period of the axis switching and the time of the split.

Large Eddy Simulation of High-Reynolds-Number Free and Wall-Bounded Flows

“…2b: jets with AR ≥ 2 are characterized by single ribs aligned with corner regions-in contrast to pairs of counterrotating ribs aligned with the corners for square jets. Other distinct topological features are associated with the occurrence of vortex ring splittings due to reconnection [50,56,58,59]. In terms of characteristic ring-rib coupling geometry, significantly larger jet spreading and 1 vorticity production in the jet for AR = 1 are shown in Fig.…”

“…The 2 -visualization approach has been shown to be ideally suited for the investigation of complex vortex topologies [54][55][56][57]. The rectangular vortex ring dynamics for AR ≥ 2 [56] is essentially the same as that of pseudoelliptic [58] and elliptic [59] rings with the same AR, after the corner regions of the rings are effectively rounded in an early vortex-ring deformation phase. Two qualitatively different ring-rib coupling geometries are shown in Fig.…”

Pinch-off of non-axisymmetric vortex rings

“…Viets & Sforza (1972) also considered the evolution of a vortex ring whose initial shape was described by a superellipse or Lamé curve. It is interesting to note that Kiya & Ishii (1991) and Kiya et al (1992) characterized the deformation of isolated 'pseudo-elliptic' vortex rings of a shape identical to those considered by Domenichini (2011).…”

Vortex ring bifurcation and secondary structures in a finite-span synthetic jet

“…However, in the present experiment -for all conditions tested -the bifurcated vortex rings diverged on outward pointing trajectories before decaying to turbulence. The collision and recombination of the bifurcated vortex rings was also not reported in the flow visualization experiments by Kambe & Takao (1971), Dhanak & Bernardinis (1981) and Kiya et al (1992) who investigated isolated vortex ring bifurcation. Several factors could explain why experimental observations have differed from simulations.…”

“…The present results may therefore represent a marginal case where vorticity reconnection occurs but is insufficiently complete to cause the vortex ring to bifurcate or cease axis switching. Kiya et al (1992) indicated this may have been the case in their complementary experiment with an AR = 8.3 pseudo-elliptic vortex ring. Therefore, we call these new regions of vorticity 'formation bridges' to differentiate them from the bridge vortices which occur after the vortex ring has switched axes.…”