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 H19: Vortex Dynamics: Dipoles, Pairs and Instabilities |
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Chair: Gerardo Chavarria, Universidad Nacional Autonoma de Mexica Room: 207 |
Monday, November 23, 2015 10:35AM - 10:48AM |
H19.00001: The evolution of a dipole in a periodic forced flow Gerardo Ruiz Chavarria, Erick Javier Lopez Sanchez, Sergio Hernandez Zapata In a tidal induced flow between a channel and an open domain a pair of counter-rotating vortices is produced during each cycle. Such pair of vortices is known as a dipole. The Strouhal number (S) is the parameter determining if dipole escapes or is sucked during the stage of negative flowrate. Some years ago an analytical model has been proposed to determine the evolution of the vortices (Wells M.G. {\&} Van Heijst G.J.F., Dynamics of atmospheres and oceans, 37(2003) 23-34). This model agrees with experimental and observational data when S is close to the critical value 0.13. However, no realistic predictions are given for small values of S. In this work we present a modification of this model to take into account some details not considered before. In particular the fact that not all vorticity created into the channel is incorporates into the dipole. This fact leads to have a lower translational velocity and also to the formation of a vorticity band behind the vortices. Our results have a better agreement with numerical simulations and experimental data. Finally we study the influence of the Reynolds number in the evolution of the vortices and the interaction between dipoles produced in subsequent cycles. [Preview Abstract] |
Monday, November 23, 2015 10:48AM - 11:01AM |
H19.00002: On the stability of a solid-body-rotation flow in a finite-length pip Shixiao Wang, Zvi Rusak, Rui Gong, Feng Liu The three-dimensional, inviscid and viscous flow instability modes that appear on a solid-body rotation flow in a finite-length, straight, circular pipe are analyzed. This study is a direct extension of the Wang \& Rusak (1996) analysis of axisymmetric instabilities on inviscid swirling flows in a pipe. We study a general mode of perturbation that satisfies the inlet, outlet and wall conditions of a flow in a finite-length pipe with a fixed-in-time and in-space vortex generator ahead of it. The eigenvalue problem for the growth rate and the shape of the perturbations for any azimuthal wave number $m$ is solved numerically for all azimuthal wave number $m$. In the inviscid flow case, the $m=1$ modes are the first to become unstable as the swirl ratio is increased and dominate the perturbation's growth in a certain range of swirl levels. In the viscous flow case, the neutral stability line is presented in a Reynolds number ($Re$) versus swirl ratio ($\omega$) diagram and can be used to predict the first appearance of of axisymmetric or spiral instabilities as a function of $Re$ and $L$. We will discuss and demonstrate the physical mechanism and evidences of the onset of the instability. [Preview Abstract] |
Monday, November 23, 2015 11:01AM - 11:14AM |
H19.00003: Evolution of Vortex Pairs Subject to the Crow Instability in Wall Effect Daniel Asselin, C.H.K. Williamson In this research, we examine the effect of a solid boundary on the dynamics and instabilities of a pair of counter-rotating vortices. An isolated vortex pair is subject to both a short-wave elliptic instability and a long-wave Crow (1970) instability. Near a wall, the boundary layer that forms between the primary vortices and the wall can separate, leading to the generation of secondary vorticity. In the present study, we are examining the long-wave Crow instability as it is modified by interaction with a wall. The regions of the perturbed vortex pair which first interact with the wall experience accelerated circulation decay, which leads to the formation of an axial pressure gradient. This pressure difference produces strong axial flows, which ultimately give rise to interactions between the primary and secondary vortices and the generation of small-scale vortex rings. These rings vary in number and orientation depending on the extent to which the Crow instability has developed prior to interaction with the wall. In addition to the topological modifications, significant changes to the vortex dynamics, including circulation and core size, are also observed during and after interaction with the boundary. [Preview Abstract] |
Monday, November 23, 2015 11:14AM - 11:27AM |
H19.00004: Moment model for interacting dipoles in two-dimensional flows Yuko Matsumoto, Kazuyuki Ueno A dynamical system for interacting dipolar vortices in two-dimensional incompressible flows is presented. Each dipole has a finite self-propelling velocity which translates itself in the direction perpendicular to the straight line between two vortices comprising the dipole in a fluid at rest. The system of interacting $N$ dipoles is described by a set of ordinary differential equations for centroids and dipole moments. This system conserves linear impulse and angular impulse. Using this system for the case of collision of two dipoles, the evolution and instability are discussed. [Preview Abstract] |
Monday, November 23, 2015 11:27AM - 11:40AM |
H19.00005: ABSTRACT WITHDRAWN |
Monday, November 23, 2015 11:40AM - 11:53AM |
H19.00006: Experimental investigation of the interaction of a vortex dipole with a deformable cantilevered plate Eugene Zivkov, Sean D. Peterson, Serhiy Yarusevych The coupled interaction of a vortex dipole impacting the tip of a deformable cantilevered plate is investigated experimentally using both flow visualization and time-resolved particle image velocimetry (PIV). Experiments are performed in shallow, density stratified salt water, which is known to reduce three-dimensional effects and maintain dipole stability through the action of buoyancy forces. The flow visualization, in which florescent dye is used to trace both the dipole and the fluid in the vicinity of the plate, is performed to elucidate the vortex dynamics upon impact. On impact, the dipole splits and forms two secondary dipoles by entraining fluid in the vicinity of the plate. The secondary dipoles follow circular trajectories and may return for subsequent impacts with the plate. PIV is employed to measure the circulation and kinetic energy of the dipole, while plate deflections extracted from sequential flow field images are used to estimate the plate strain energy. By analyzing the results obtained on a rigid and compliant plate, the effect of compliance on the attendant vortex dynamics is investigated. The results are compared with previously published numerical simulations and conclusions are drawn with regards to energy harvesting from vortices using smart materials. [Preview Abstract] |
Monday, November 23, 2015 11:53AM - 12:06PM |
H19.00007: A Quantitative Assessment of Asymmetric Vortex Interactions in Viscous Flow Patrick Folz, Keiko Nomura The interactions of two co-rotating vortices in viscous fluid are investigated using 2D numerical simulations, performed across a range of vortex strength ratios, $\Lambda = \Gamma_1/\Gamma_2$, with differing initial size and/or peak vorticity. In all cases, the interaction produces a single vortex which is quantitatively evaluated, in particular in terms of an enhancement factor, $\varepsilon = \Gamma_{final}/\Gamma_{initial}$, akin to what has previously been done for inviscid flow. The analysis monitors the vortex cores throughout the interaction and identifies the end of the interaction, at which time the existing vortex is assessed. Symmetric pairs produce a compound vortex with $\varepsilon$ near the maximum value of $2$. For asymmetric pairs, $\varepsilon$ and the associated merging efficiency generally decrease with $\Lambda$, although differing pairs with the same $\Lambda$ may produce different outcomes. For significantly disparate vortices, one of the original vortices survives without enhancement, i.e., $\varepsilon \sim 1$. These observations are explained in terms of underlying physics. Comparisons are made with available experimental data. [Preview Abstract] |
Monday, November 23, 2015 12:06PM - 12:19PM |
H19.00008: Transient wake and trajectory of free falling cones with various apex angles Yaqing Jin, Ali M. Hamed, Leonardo P. Chamorro The early free-fall stages of cones with a density ratio 1.18 and apex angles of 30$^{\mathrm{o}}$, 45$^{\mathrm{o}}$, 60$^{\mathrm{o}}$, and 90$^{\mathrm{o}}$ were studied using a wireless 3-axis gyroscope and accelerometer to describe the cone 3D motions, while the induced flow in the near wake was captured using particle image velocimetry. The Reynolds number based on the cone diameter and the velocity at which the cone reaches the first local velocity maximum is found to set the limit between two distinctive states. Before this Re is reached the departure from the vertical path and cone rotations are insignificant, while relatively rapid growth is observed after this Re. Sequences of vertical velocity, swirling strength, LES-decomposed velocity, and pressure fields shows the formation and growth of a large and initially symmetric recirculation bubble at the cone base and highlights the presence of a symmetric 3D vortex rollup dominating the near-wake in the early stages of the fall. Later, the shear layer at the edge of the wake manifests in the shedding of Kelvin-Helmholtz vortices that, due to the nature of the recirculation bubble, reorganize to constitute a part of the rollup. Later in the fall, the wake loses its symmetry and shows a high population of vortical structures leading to turbulence. The asymmetric wake leads to strong interactions between the flow field and the cone creating complex feedback loops. [Preview Abstract] |
Monday, November 23, 2015 12:19PM - 12:32PM |
H19.00009: Late time vortex dynamics for a coherent structure interacting with fine-scale turbulence Eric Stout, Fazle Hussain The vortex dynamics of perturbations to a coherent vortex column with fine-scale turbulence induced axial flow are examined using direct numerical simulation. Turbulence forms into azimuthally oriented filaments, which naturally results in axial flow as the filaments self-advect. Axial flow ($W)$ modifies vorticity generation in two ways: 1) the radial gradient of $W$ causes radial perturbation vorticity to tilt into the axial direction; and 2) axial perturbation vorticity tilts mean azimuthal vorticity (the vortical equivalent of $W)$ into the radial direction. Given the cycle of radial and axial perturbation vorticity generation, with the concomitant generation of azimuthal vorticity by the column's mean strain, this provides a physical explanation for instability due to axial flow (i.e. instability of the Batchelor or $q$-vortex, where $q$ is the ratio of peak azimuthal to peak axial velocities). Via this interpretation, the role of non-axisymmetric azimuthal modes in $q$-vortex instability is explained. Vorticity generation due to axial flow is explored using a simplified perturbation consisting of two, antiparallel helical vortex threads encircling a vortex column, which results in late time vorticity generation and energy production. [Preview Abstract] |
Monday, November 23, 2015 12:32PM - 12:45PM |
H19.00010: Experimental investigation of boundary layer transition on rotating cones in axial flow in 0 and 35 degrees angle of attack Ali Kargar, Kamyar Mansour In this paper, experimental results using hot wire anemometer and smoke visualization are presented. The results obtained from the hot wire anemometer for critical Reynolds number and transitional Reynolds number are compared with previous results. Excellent agreement is found for the transitional Reynolds number. The results for the transitional Reynolds number are also compared to previous linear stability results. The results from the smoke visualization clearly show the crossflow vortices which arise in the transition process from a laminar to a turbulent flow. A non-zero angle of attack is also considered. we compare our results by linear stability theory which was done by. We just emphasis. Also we compare visualization and hot wire anemometer results graphically, our goal in this paper is to check reliability of using hot wire anemometer and smoke visualization in stability problem and check reliability of linear stability theory for this two cases and compare our results with some trusty experimental works. [Preview Abstract] |
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