Bulletin of the American Physical Society
67th Annual Meeting of the APS Division of Fluid Dynamics
Volume 59, Number 20
Sunday–Tuesday, November 23–25, 2014; San Francisco, California
Session E21: Instability: Vortex Flows |
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Chair: Paul Fontana, Seattle University Room: 2010 |
Sunday, November 23, 2014 4:45PM - 4:58PM |
E21.00001: Two-dimensional linear instability of a Lamb-Oseen counter-rotating vortex dipole Remi Jugier, Laurent Joly, Jerome Fontane, Pierre Brancher The present study investigates the stability of a family of quasi-steady two-dimensional vortex dipoles resulting from the adaptation to the mutual deformation and viscous diffusion of counter-rotating Lamb-Oseen vortices of equal size and circulation. For sufficiently large Reynolds numbers, the internal structure is set by the dipole aspect ratio $a/b$ (radius versus separation distance), giving rise to a family of smooth quasi-steady solutions. These base flow solutions consist of self-propagating dipoles with a vorticity trail leaking from the dipole during the self-adaptation process and from diffusion across the dipole Kelvin oval. The present work is a generalization of the recent study by Brion \textit{et al.} (Phys. Fluids 2014), who found that a specific kind of vortex dipole, the Lamb-Chaplygin dipole, was unstable with respect to two-dimensionnal perturbations. We show how the growth rate and spatial structure of the unstable modes vary with aspect ratio $a/b$ and Reynolds number. The growth rates are lower than for the Lamb-Chaplygin dipole and decreases when the aspect ratio is lowered. It is advocated here that these new two-dimensional modes of small aspect-ratio smooth dipoles are good candidates for steady actuation in aircrafts conditions. [Preview Abstract] |
Sunday, November 23, 2014 4:58PM - 5:11PM |
E21.00002: Experimental and theoretical analysis of vortex breakdown in the wake of the $25^{\circ}$ Ahmed body Cyril Jermann, Philippe Meliga, Gregory Pujals, Francois Gallaire, Eric Serre We study experimentally and theoretically the wake of the $25^o$ Ahmed body, considered a suitable test-case to reproduce the two counter-rotating longitudinal vortices widely encountered in automotive aerodynamics. The three-dimensional experimental mean flow is reconstructed at high Reynolds number ($Re = 2.8 \times 10^6$) from a series of cross-flow time-averaged planes acquired with a moving automated Stereo-PIV system. We observe a sharp decay of the axial velocity and vorticity in the near-wake, $0.5$ times the projected length of the slanted surface downstream the square back, where the streamwise vortices is subjected to a strong adverse pressure gradient and the turbulent kinetic energy exhibits a peak in the vortex core. A stability analysis of the experimental velocity shows that the flow undergoes vortex breakdown roughly at the same position, through a transition from supercritical ($x < 0.5$) to subcritical ($x > 0.5$) conditions and the accumulation of upstream propagating axisymmetric waves. [Preview Abstract] |
Sunday, November 23, 2014 5:11PM - 5:24PM |
E21.00003: The linear stability analysis of swirling flows in a finite-length pipe Rui Gong, Shixiao Wang, Zvi Rusak The linear stability of an inviscid, axisymmetric and rotating columnar flow in a finite length pipe against general type of perturbations is studied. The perturbation mode is subject to a set of boundary conditions that may reflect the physical situation of the swirling flow in a finite-length pipe. This type of stability problem was first studied by Wang and Rusak (1996). The current study generalized their original analysis (valid for axisymmetric perturbations) to a stability analysis of general type of perturbations. The underlying physical mechanism of the unstable mode is examined and discussed in terms of the energy transfer mechanism between the perturbations and the base flow. [Preview Abstract] |
Sunday, November 23, 2014 5:24PM - 5:37PM |
E21.00004: Onset of unsteady flow in wavy walled channels at low Reynolds number Tapan Shah, Zachary Mills, Alexander Alexeev Using computational modeling, we examine the development of an unsteady laminar flow of a Newtonian fluid in a channel with sinusoidal walls, driven by a constant pressure gradient. The lattice Boltzmann method was used as our computational model. Our simulations revealed two types of unsteady flows occurring in sinusoidal channels. When the amplitude of the wavy walls is relatively small, vortices forming in the channel furrows are shed downstream. For larger wall wave amplitudes, vortices remain inside the furrows and exhibit periodic oscillations and topological changes. Our simulations establish the optimum wall amplitude and period leading to an unsteady flow at the minimum pressure gradient. The results are important for designing laminar heat/mass exchangers utilizing unsteady flows for enhancing transport processes. [Preview Abstract] |
Sunday, November 23, 2014 5:37PM - 5:50PM |
E21.00005: Numerical Study of Electrolytic Flow Instabilities Driven by an Azimuthal Lorentz Force in a Cylindrical Geometry James P\'erez-Barrera, Jos\'e Enrique P\'erez-Espinoza, Alejandro Ort\'Iz, Sergio Cuevas, Eduardo Ramos We present numerical simulations of the flow produced by an azimuthal Lorentz force in an electromagnetic stirrer. The stirrer consists of a cylindrical cavity with two copper concentric cylindrical electrodes, filled with an electrolytic solution. Underneath the cavity, a permanent magnet creates an almost uniform magnetic field, perpendicular to the circular section of the stirrer. An electric potential difference between the electrodes produces a radial D.C. current that passes through the fluid and interacts with the axial magnetic field, generating an azimuthal Lorentz force that drives the fluid. Experiments have shown the appearance of a flow instability that gives rise to a varying number of anticyclonic vortices for given values of the current intensity and fluid layer thickness. The MHD governing equations are expressed in terms of the velocity, pressure and electric potential. Numerical simulations are carried out using a hybrid Finite volume-Fourier method to ensure periodicity in the azimuthal direction. Numerical results show the formation of different modes of perturbation in the velocity field, which give rise to a varying number of traveling vortical structures. [Preview Abstract] |
Sunday, November 23, 2014 5:50PM - 6:03PM |
E21.00006: Anomalous vortex shedding and wake profiles in quasi-two-dimensional flows Paul W. Fontana, Dominic A. Dams Vortex shedding by circular cylinders in a vertical soap film channel exhibits anomalously low shedding frequencies compared with observations in conventional systems. Furthermore, the Strouhal number ($\mbox{St} = fD/U_\infty$, where $f$ is the shedding frequency, $D$ the cylinder diameter, and $U_\infty$ the upstream flow speed) is not uniquely determined by the Reynolds number ($\mbox{Re} = DU_\infty/\nu$, where $\nu$ is the kinematic viscosity). We have previously argued that Ekman friction is a likely cause [\textit{Bull.\ Amer.\ Phys.\ Soc.}\ \textbf{57}(17), R10.7]. Other possibilities include gravity, which in this system acts as a forcing mechanism not typically present during vortex shedding measurements, surface tension effects, or variable-viscosity effects due to variations in film thickness. Theory to predict the shedding frequency is lacking and so it is unclear if or how each of these mechanisms should affect it, but understanding the anomaly may elucidate the shedding process. We present two-dimensional profiles of velocity, viscosity, and surface friction measured in the wake of the cylinder under several sets of flow parameters and discuss their implications for the various candidates. The results do not support variable viscosity as a cause. [Preview Abstract] |
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