Bulletin of the American Physical Society
68th Annual Meeting of the APS Division of Fluid Dynamics
Volume 60, Number 21
Sunday–Tuesday, November 22–24, 2015; Boston, Massachusetts
Session L19: Vortex Dynamics: Vortex Rings |
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Chair: Bartosz Protas, McMaster University Room: 207 |
Monday, November 23, 2015 4:05PM - 4:18PM |
L19.00001: Linear Stability of Hill's Vortex to Axisymmetric Perturbations Bartosz Protas We consider the linear stability of Hill's vortex with respect to axisymmetric perturbations. Given that Hill's vortex is a solution of a free-boundary problem, this stability analysis is performed by applying methods of shape differentiation to the contour dynamics formulation of the problem in a 3D axisymmetric geometry. It allows us to systematically account for the effect of boundary deformations on the linearized evolution of the vortex. The resulting singular integro-differential operator defined on the vortex boundary is discretized with a spectral approach. This operator has two unstable and two stable eigenvalues complemented by a continuous spectrum of neutrally-stable eigenvalues. By considering a family of suitably regularized (smoothed) problems we demonstrate that the corresponding eigenfunctions are in fact singular objects in the form of infinitely sharp peaks localized at the front and rear stagnation points. These findings thus refine the results of the classical analysis by Moffatt \& Moore (1978). [Preview Abstract] |
Monday, November 23, 2015 4:18PM - 4:31PM |
L19.00002: An experimental study on the formation of negatively-buoyant vortex rings Jeff X. Wu, Gary R. Hunt Experiments to examine the formation of dense saline vortex rings projected vertically upwards into a quiescent freshwater environment were conducted. The setup was designed to dispense a cylindrical column of source fluid with aspect ratio $L/D$ (the length $L$ of dispensed saline column to the nozzle diameter $D$) over a pre-set time interval. In an effort to execute an impulsive start and finish, a controlled flow circulation driven by a gear pump was developed to approximate a top-hat profile of source exit velocity versus time. Our measurements focus on describing the evolving morphology of the vortex rings with time and with source conditions ($L/D$ and source Froude number). Our results reveal distinct formation regimes and our estimates of time required for formation as a function of density difference confirm predictions from previously published numerical simulations. The volume-based approach we adopt provides potentially a new angle for investigating the physics of these flows. [Preview Abstract] |
Monday, November 23, 2015 4:31PM - 4:44PM |
L19.00003: The effect of entrainment on starting vortices Giuseppe Rosi, David Rival Recent work shows that vortex detachment behind accelerating plates coincides with when streamlines enclosing the starting vortex (SV) form a full saddle.\footnote{Rival, D. E. et al., \textit{Exp. In Fluids}, 55:1660 (2014).} In the case of a linearly accelerating plate, it can be shown that vorticity-containing mass, and thus the SV's development scale with only dimensionless towed distance, while the SV's circulation scales with the acceleration rate. This results in shear-layer instabilities whose structure is Reynold-number independent, but whose strength scale with Reynolds number. It is hypothesized that the increased strength of the instabilities promotes entrainment, which causes the formation of the full saddle and thereby detachment to occur at an earlier dimensionless towed distance. To test this hypothesis, a circular plate is linearly accelerated from rest to pinch-off with chord-based Reynolds numbers of 10$^{3}$, 10$^{4}$, and 10$^{5}$ at the midpoint of the motion. Planar PIV data is acquired, from which FTLE and enstrophy fields are calculated. Vortex detachment is identified from the dynamics of the FTLE saddles, while the enstrophy fields are used to calculate both the vorticity-containing mass entering from the shear layer and the mass entrained from the quiescent surroundings. [Preview Abstract] |
Monday, November 23, 2015 4:44PM - 4:57PM |
L19.00004: The effect of aspect ratio on vortex pinch-off over laminar and turbulent regimes John Fernando, David Rival In the current study, vortex rings formed behind accelerating flat plates are investigated to determine the role of aspect ratio on pinch-off over a range of 10$^{3} \quad \le $ Re $\le $ 10$^{5}$. We begin by demonstrating that aspect ratio plays a primary role in pinch-off, while the role of plate-edge curvature is of secondary importance. For vortex rings produced in the wake of elliptical plates (AR\textgreater 1), the point of vortex pinch-off has been shown to be coterminous with the formation of a pressure maximum between the vortex ring and shear layer, as the elliptical ring deforms away from the feeding source. For the circular plate (AR$=$1), pinch-off is not clearly identified, and the vortex ring eventually breaks down in the wake. It is hypothesized that with increasing Reynolds number the vortex rings develop more quickly due to increased levels of mixing (entrainment) across the shear-layer interface. As such, vortex pinch-off is hastened for the circular plate with increasing Reynolds number, yet remains unchanged for the elliptical plate, for which the timescales of vortex-ring deformation (i.e. detachment) are faster than the rate of fluid entrainment. Force and velocimetry measurements are used to support this hypothesis. [Preview Abstract] |
Monday, November 23, 2015 4:57PM - 5:10PM |
L19.00005: Interaction of Vortex Ring with Cutting Plate Mustafa Musta The interaction of a vortex ring impinging on a thin cutting plate was made experimentally using Volumetric 3-component Velocitmetry (v3v) technique. The vortex rings were generated with piston-cylinder vortex ring generator using piston stroke-to-diameter ratios and Re at 2-3 and 1500 - 3000, respectively. The cutting of vortex rings below center line leads to the formation of secondary vortices on each side of the plate which is look like two vortex rings, and a third vortex ring propagates further downstream in the direction of the initial vortex ring, which is previously showed by flow visualization study of Weigand (1993) and called ``trifurcation''. Trifurcation is very sensitive to the initial Reynolds number and the position of the plate with respect to the vortex ring generator pipe. The present work seeks more detailed investigation on the trifurcation using V3V technique. Conditions for the formation of trifurcation is analyzed and compared with Weigand (1993). The formed secondary vortex rings and the propagation of initial vortex ring in the downstream of the plate are analyzed by calculating their circulation, energy and trajectories. [Preview Abstract] |
Monday, November 23, 2015 5:10PM - 5:23PM |
L19.00006: The dynamics of a vortex ring crossing at density interface Roberto Zenit, John Dabiri We examine the process of an isolated vortex ring crossing the interface between two stratified miscible liquids. Using both planar induced fluorescence and particle image velocimetry, we study the evolution of the ring while crossing the interface considering positive and negative density contrasts. The velocity, density and pressure fields are determined; therefore, it is possible to track the evolution of the vorticity field and the baroclinic torque. We found that the process of baroclinic vorticity production is different for upward or downward moving vortices (from dense to light and from light to dense fluids). Some preliminary results will be discussed. These results could be of importance in the understanding of mixing is stratified environments. [Preview Abstract] |
Monday, November 23, 2015 5:23PM - 5:36PM |
L19.00007: High-Speed 3D Visualization of the Head-on Collision of Vortex Rings Ryan McKeown, Shmuel Rubinstein The head-on collision between two laminar vortex rings results in a complex dynamic pattern that has been previously observed, though never fully explained. During their initial interaction, the laminar vortex rings elongate radially along the collision plane, while the two vortex cores approach one another. When the distance between the vortex cores reaches a critical length scale, they either reconnect into secondary vortex rings or break down and dissipate into a turbulent cloud, depending on their initial Reynolds number. By filming this collision at high speeds, while illuminating it with a scanning laser sheet, we can reconstruct the intricate three-dimensional flow structure at the collision plane. We find that the onset of the vortex ring breakdown is triggered by a sequential cascade of instabilities that interact with the vortex cores. Understanding the role of these instabilities in the breakdown of vortex rings could provide new insight into the evolution and stabilization of vortices. [Preview Abstract] |
Monday, November 23, 2015 5:36PM - 5:49PM |
L19.00008: Interaction of multiple co-axial co-rotating vortex rings Suyang Qin, Hong Liu, Xiaoyu Liu, Yang Xiang Fish and birds gain hydrodynamic force from a wake of discrete or linked vortex chain, which is the existence form of vortex rings in nature. Vortex rings with the same formation time are generated successively with different time interval by a piston-cylinder arrangement, and the velocity fields are measured using DPIV. The motion of multiple interacting vortex rings is first reported in laboratorial experiments. Besides the most attracting leapfrogging phenomenon, two other phenomena, suction and weak influence, are also clearly presented using the method of Lagrangian coherent structures. Due to the induced effect of wake vortex rings, the formation process of the forming vortex rings is different from that of a single isolated vortex ring, indicating that another distinct timescale exists, together with formation number proposed by Gharib (1998 JFM), determining the mechanisms of vortex rings. When the rear vortex ring leapfrogs, the limiting case is that the rear contracting ring is axis-touching. If an axis-touching ring is further squeezed by the wake vortex, the vortex structure will collapse, which can be explained by Kelvin–Benjamin variational principle. According to this principle, it is impossible for two optimal formed vortex rings to leapfrog. [Preview Abstract] |
Monday, November 23, 2015 5:49PM - 6:02PM |
L19.00009: Force due to vortex ring impact Daniel Andrus, Rhett Jefferies, Michael Krane The impact force of a vortex ring collision on a solid surface is presented. The focus of this study is to estimate the unsteady wall pressure distribution from time-varying velocity fields. The velocity fields are produced analytically after a Lagrangian computation of the vorticity in the vortex ring is performed. Two pressure estimations are used in this study. The first is a discretized green's function solution of Poisson's equation for total pressure (Hofmans, 1998). The second (Dabiri, et al., 2014) integrates the acceleration, estimated from the material derivative of the discrete velocity field. These analytical estimations are compared with one another and to experimental data (McErlean, 2011). [Preview Abstract] |
Monday, November 23, 2015 6:02PM - 6:15PM |
L19.00010: Impact of a vortex ring on a wall with a circular cutout JiaCheng Hu, Sean D. Peterson The rising interests in the development of small-scale energy harvesters have prompted research efforts into fluid interactions with highly deformable materials, with a few studies utilizing vortex rings as the energy source. In particular, Hu et al. (JIMSS, 2014) investigated a vortex ring impacting a concentric deformable annulus and found that a smaller ring appears and propagates away post impact. However, due to the fixture of the structure, the interaction process was not captured. The present study is a follow-up experiment to elucidate the smaller ring formation using a rigid wall with a circular cutout. We observe that the smaller ring is formed out of the induced vorticity at the cutout tip. Furthermore, despite the cutout, the classical vortex ring - wall interaction still occurs, wherein the induced boundary layer on the impact side of the wall ejects secondary and tertiary rings near the wall. Interestingly, when the cutout is shifted off-center, the wall splits the original ring into two portions. The portion that passes through the hole connects with the induced vorticity at the cutout tip, forms a new ring, and propagates away at an angle; the blocked portion follows the classical vortex ring - wall interaction. [Preview Abstract] |
Monday, November 23, 2015 6:15PM - 6:28PM |
L19.00011: Evolution of an elliptic vortex ring in a viscous fluid Jing Lou, Ming Cheng, T.T. Lim The evolution of a viscous elliptic vortex ring in an initially quiescent fluid or a linear shear is numerically simulated. A wide range of parameters are considered, for aspect ratios (AR) (1 $\le $ AR $\le $ 8),radius to ring radius ratios (\textbf{0}) (0.1 $\le $ \textbf{0 }$\le $ 0.3), Reynolds number (Re) (500 $\le $ Re $\le $ 3000)shear rate (K) (0 $\le $ K $\le $ 0.12). The study aims to fill the gap in the current knowledge of dynamics of an elliptic vortex ring in a viscous fluid and also to address the issue of whether elliptic ring undergoes vortex stretching and compression during axis-switching. In a quiescent, results show that there exists a critical aspect ratio (ARc), below which an elliptic ring undergoes oscillatory deformation with the period that increases with decreasing AR. Above ARc, the vortex ring breaks up into two or three sub-rings after the first half-cycle oscillation. While higher Reynolds number enhances vortex ring breakup, larger core size has opposite effect. Contrary to an inviscid theory, an elliptic ring does undergo vortex stretching compression during oscillatory deformation. In the presence of a linear shear flow, the vortex undergoes not only oscillatory deformation and stretching but also tilting as it propagates. [Preview Abstract] |
Monday, November 23, 2015 6:28PM - 6:41PM |
L19.00012: The analytical model for vortex ring pinch-off process based on the energy extremum principle Yang Xiang, Hong Liu, Suyang Qin, Fuxin Wang The discovery of vortex ring pinch-off is greatly helpful for us to understand the mechanism of optimal vortex formation, which further implies the optimal biological propulsion for animals. The vortex ring pinch-off implies its limiting formation and is dominated by the energy extremum principle. However, it is found that vortex ring pinch-off is a continuous process rather than a transient timescale. Therefore, we are wondering that how to identify the onset and end of pinch-off process. Based on the Kelvin-Benjamin variational principle, a dimensionless energy number is adopted to characterize the energy evolution of vortex rings. The vortex ring flow fields are obtained by DPIV with the piston-cylinder setup, and their geometric structures are identified using its Lagrangian coherent structures. The results show that the dimensionless energy numbers with the steady translating vortex rings share a critical value. It is then demonstrated that the dimensionless energy number dominates the onset and the end of pinch-off process. Besides, the onset and end of pinch-off can also be identified using LCSs. Additionally, based on the dimensionless energy number or LCSs, the corresponding vortex ring formation times(L/D) for the onset or the end of pinch-off are consistent. [Preview Abstract] |
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