Bulletin of the American Physical Society
69th Annual Meeting of the APS Division of Fluid Dynamics
Volume 61, Number 20
Sunday–Tuesday, November 20–22, 2016; Portland, Oregon
Session H3: Vortex Dynamics: Vortex Rings |
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Chair: C.H.K Williamson, Cornell University Room: B110-111 |
Monday, November 21, 2016 10:40AM - 10:53AM |
H3.00001: Impingement of a Vortex Pair on a Wavy Wall Sarah Morris, C.H.K. Williamson In this research we examine the impingement of a vortex pair onto a wavy wall. Isolated vortex pairs, not in ground effect, can become unstable to short-wave (Widnall, 1974) or long-wave instability (Crow, 1970). When a vortex pair approaches a ground plane, the boundary layer that forms on the surface separates, generating secondary vorticity and causing the primary pair to `rebound'. When a vortex pair with the long-wave instability interacts with a flat boundary, the topology of the pair changes, resulting in rebounding vortical structures whose form is dependent on the extent of the instability prior to wall interaction (Asselin {\&} Williamson, 2013, 2016). By using PIV and LIF to consider the "complementary" experiment, a straight vortex pair encountering a wavy wall (rather than a wavy pair impinging on a flat wall), certain critical features of the two flows are found to be similar. The 2D vortex pair first interacts with the ``hills'' of the boundary, triggering accelerated vorticity cancellation in this area compared to the corresponding ``valley'' regions. An axial pressure gradient forms between the two regions, giving rise to strong axial flow. This leads to the interaction of primary and secondary vortices in the valleys, wherein reconnection results in "rebounding" vortex rings, two per fundamental wavelength. The resulting flowfield forms distinctly different vortex structures than are classically found for 2D vortex pair wall impingement or for the long-wave instability out of ground effect. [Preview Abstract] |
Monday, November 21, 2016 10:53AM - 11:06AM |
H3.00002: Formation number for vortex dipoles Vahid Sadri, Paul S Krueger This investigation considers the axisymmetric formation of two opposite sign concentric vortex rings from jet ejection between concentric cylinders. This arrangement is similar to planar flow in that the vortex rings will travel together when the gap between the cylinders is small, similar to a vortex dipole, but it has the advantage that the vortex motion is less constrained than the planar case (vortex stretching and vortex line curvature is allowed). The flow was simulated numerically at a jet Reynolds number of 1,000 (based on $\Delta R$ \begin{figure}[htbp] \centerline{\includegraphics[width=0.21in,height=0.20in]{020820161.eps}} \label{fig1} \end{figure} and the jet velocity), jet pulse length-to-gap ratio ($L/\Delta R)$ in the range 10--20, and gap-to-outer radius ratio ($\Delta R/R_{o})$ in the range 0.01-0.1. Small gap ratios were chosen for comparison with 2D results. In contrast with 2D results, the closely paired vortices in this study exhibited pinch-off from the generating flow and finite formation numbers. The more complex flow evolution afforded by the axisymmetric model and its influence on the pinch-off process will be discussed. [Preview Abstract] |
Monday, November 21, 2016 11:06AM - 11:19AM |
H3.00003: Vortex ring formation in starting forced plumes with negative and positive buoyancy Lei Gao, Simon Ching-Man Yu The limiting process of vortex formation in starting forced plumes, with Richardson number in the range of $-$0.06 $\le $ Ri $\le $ 0.06, was studied numerically. As Ri increases, three regimes can be identified in terms of the vortex interaction patterns, i.e., the weak-interaction regime ($-$0.06 \textless Ri \textless $-$0.02), the transition regime ($-$0.02 $\le $ Ri \textless 0) and the strong-interaction regime (0 $\le $ Ri \textless 0.06). The numerical results show that the variation trends of formation number and separation number against Ri change near the critical value of $-$0.02. In the weak-interaction regime, both formation number and separation number increase rapidly against Ri. In the transition and strong-interaction regimes alike, the formation number increases at a much slower rate, while the separation number declines dramatically as Ri increases. A qualitative explanation on the variation patterns of formation number and separation number is proposed based on the buoyancy effects on the dynamic properties of the leading vortex ring and the vortex interaction patterns. [Preview Abstract] |
Monday, November 21, 2016 11:19AM - 11:32AM |
H3.00004: Drift due to viscous vortex rings Thomas Morrell, Saverio Spagnolie, Jean-Luc Thiffeault Biomixing is the study of fluid mixing due to swimming organisms. While large organisms typically produce turbulent flows in their wake, small organisms produce less turbulent wakes; the main mechanism of mixing is the induced net particle displacement (drift). Several experiments have examined this drift for small jellyfish, which produce vortex rings that trap and transport a fair amount of fluid. Inviscid theory implies infinite particle displacements for the trapped fluid, so the effect of viscosity must be included to understand the damping of real vortex motion. We use a model viscous vortex ring to compute particle displacements and other relevant quantities, such as the integrated moments of the displacement. Fluid entrainment at the tail end of a growing vortex `envelope' is found to play an important role in the total fluid transport and drift. [Preview Abstract] |
Monday, November 21, 2016 11:32AM - 11:45AM |
H3.00005: Buoyant vortex rings and knots with thin core Ching Chang, Stefan Llewellyn Smith One challenge of studying the motion of vortex filaments arises from the singular nature of the Biot-Savart integral. We employ the momentum balance investigated by Moore and Saffman for thin-core vortex filaments to obtain the self-induced velocity of filaments, rings and knots. A key feature of the approach is the possibility of incorporating buoyancy forces. The numerical scheme used is discussed and compared to previous analytical and numerical results in the literature. The effect of geometry and buoyancy on the motion of such vortices is examined. [Preview Abstract] |
Monday, November 21, 2016 11:45AM - 11:58AM |
H3.00006: Experimental study of vortex ring interactions with a flexible beam; investigating the role of viscous effects. Alireza Pirnia, JiaCheng Hu, Sean Peterson, Byron Erath Energy can be extracted from flow instabilities in the environment for powering low consumption devices. When vortices pass tangentially over a flexible beam the lower pressure in the vortex core causes the beam to deflect, and induces sustained oscillations which can be converted into energy via piezoelectric materials. The beam dynamics can be parameterized according to the beam properties (nondimensional mass and stiffness ratios) as well as the vortex properties (size, vortex circulation strength and advection velocity). Recently, inviscid models have been developed to solve this fluid-structure interaction problem but they do not capture viscous interactions; features that become more prominent when the beam is positioned close to the vortex core. In this study the interaction of a vortex ring passing tangentially over a flexible beam as a function of circulation strength, beam properties, and offset distance are investigated to identify how viscous interactions influence the energy exchange process. Particle image velocimetry is acquired in tandem with the beam dynamics. The velocity and pressure fields, and transient beam dynamics are compared and contrasted with an inviscid model to identify the role of viscous interactions. [Preview Abstract] |
Monday, November 21, 2016 11:58AM - 12:11PM |
H3.00007: Direct numerical simulations of vortex ring collisions Rodolfo Ostilla Monico, Alain Pumir, Michael Brenner We numerically simulate the ring vortex collision experiment of Lim and Nickels (Nature, 357:225-227, 1992) in an attempt to understand the rapid formation of very fine scale turbulence (or 'smoke') from relatively smooth initial conditions. Reynolds numbers of up to $Re=\Gamma/\nu=7500$, where $\Gamma$ is the vortex ring circulation and $\nu$ the kinematic viscosity of the fluid are reached, which coincide with the highest Reynolds number case of the experiments. Different perturbations to the ring vortex are added, and their effect on the generation and amplification of turbulence is quantified. The underlying dynamics of the vortex core is analyzed, and compared to the dynamics arising from a simple Biot-Savart filament model for the core. [Preview Abstract] |
Monday, November 21, 2016 12:11PM - 12:24PM |
H3.00008: Numerical study of asymmetrical modes in a vortex ring impacting a conical surface Jose Antonio Trejo Gutierrez, Erick Javier Lopez Sanchez, Sergio Hernandez Zapata, Gerardo Ruiz Chavarria In this work we investigate the impact of an annular vortex on a conical surface when their symmetry axes are parallel but they do not coincide. For this purpose we solve the Navier-Stokes and continuity equations in cylindrical coordinates. We use a finite difference scheme for r and z coordinates whereas for the angular coordinate we use a Fourier spectral method. We study the development of asymmetrical modes when the vortex approaches the inner surface of the cone. The presence of the vortex ring induces the formation of a boundary layer which detaches and leads to the formation of a secondary vortex of opposite sign which moves away the cone. This secondary vortex also exhibits asymmetrical modes, which are attenuated as it moves. We present some results as the trajectories of the primary and the secondary vortices, their circulations as a function of time, the development of asymmetrical modes and the dependence of these properties on the Reynolds number and the distance between both symmetry axes. Finally we made a comparison of primary and secondary vortices with a free vortex. [Preview Abstract] |
Monday, November 21, 2016 12:24PM - 12:37PM |
H3.00009: Gap vortex streets and turbulence in time-dependent streams Dan Duong, Stavros Tavoularis Gap vortex streets form in axial flows in highly eccentric annular channels, tightly packed rod bundles and other channels having narrow gap regions flanked by wider ones. The characteristics of these vortices and the flow and turbulence distributions in some of these channels have in the past documented for steady streams; in particular, the vortex generation frequency was found to be proportional to the bulk Reynolds number. The present study extends these findings to both accelerating and decelerating air flows in a large-scale rod bundle, configured as a wind tunnel with a by-pass branch equipped with a controlled movable flap just downstream of the blower. Time-dependent statistical properties in a gap and a subchannel centre were determined by phase-averaging velocity measurements collected with hot-wire anemometers and the time history of the phase-averaged vortex street frequency was determined with the use of a wavelet transform. Contrary to expectations, the results show that deviations of the vortex frequency and other flow characteristics from the corresponding values in steady flows at the same bulk Reynolds number were significant during acceleration and much less so during deceleration. [Preview Abstract] |
Monday, November 21, 2016 12:37PM - 12:50PM |
H3.00010: Stratified Vortex Rings: Visualization of the Density Evolution Jason Olsthoorn, Stuart Dalziel The study of vortex-ring induced stratified mixing has played a key role in understanding stratified turbulent mixing. In this study, we present an experimental investigation of the mechanical evolution and the stratification-modified three-dimensional instability of these vortex rings. Using a stereoscopic particle image velocimetry setup, we reconstruct a full, three-dimensional, time-resolved velocity field of the interaction of a vortex ring with a stratified interface. This reconstruction agrees with previous two-dimensional studies, while capturing the three-dimensional instabilities of the dynamical evolution. The stratified three-dimensional instability of a vortex ring is similar to the unstratified instability, but here the instability occurs much earlier. Through the use of numerical integration, we use the experimentally determined velocity field to simulate the kinematic evolution of the density stratification. This technique allows us to evaluate the vertical buoyancy flux throughout the vortex-ring interaction, providing a quantitative explanation for the interface sharpening observed within the experiments. Understanding the sharpening mechanism in the context of a vortex ring has direct relevance to understanding the layer formation found in stratified turbulence [Preview Abstract] |
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