Bulletin of the American Physical Society
60th Annual Meeting of the Divison of Fluid Dynamics
Volume 52, Number 12
Sunday–Tuesday, November 18–20, 2007; Salt Lake City, Utah
Session JR: Vortex Dynamics and 3D Vortex Flows VI |
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Chair: Michael Siegal, New Jersey Institute of Technology Room: Salt Palace Convention Center 251 F |
Monday, November 19, 2007 3:35PM - 3:48PM |
JR.00001: Evolution of a dipole in two-dimensional flows Yuko Matsumoto, Tsunenari Saito, Kazuyuki Ueno A simple model for the motion of a dipole in background flows is presented. The dipole is characterized by three time-dependent variables: position, dipole moment and radius. The motion of a dipole is described by the system of differential equations for the characteristic variables, which are derived from the conservation of momentum and Kelvin's circulation theorem. The equations predict analytically that the evolution of the dipole depends on the velocity gradient of the ambient flow along dipole's axis. For the case of that the velocity gradient is positive, the dipole should be stretched in its axis direction. On the other hand, when the velocity gradient is negative, vortices of the dipole will be separated. These predictions are confirmed by numerical simulations with the vortex method. [Preview Abstract] |
Monday, November 19, 2007 3:48PM - 4:01PM |
JR.00002: Electromagnetically driven dipolar vortices in shallow fluid layers Sergio Cuevas, Aldo Figueroa, Francois Demiaux, Eduardo Ramos Steady dipolar vortices continuously driven by electromagnetic forcing in a shallow layer of an electrolytic fluid are studied experimentally and theoretically. The driving Lorentz force is generated by the interaction of a D.C. uniform electric current injected in the thin layer and the magnetic field produced by a small dipolar permanent magnet. Using Particle Image Velocimetry, velocity profiles in the neighbourhood of the zone affected by the non-uniform magnetic field were obtained in planes parallel to the bottom wall, as well as in planes normal to this wall. A quasi-two-dimensional finite difference numerical model, based on the low-magnetic Reynolds number approximation, was developed to describe the experimental results. The Navier-Stokes equation includes not only the forcing term due to the injected current but also a term that involves induced currents and that brakes the flow in the bulk. The effect of the bottom wall was modeled through a Hartmann-Rayleigh friction term that accounts for both the Hartmann braking within the zone of high magnetic field strength and the viscous Rayleigh friction in regions where the magnetic field is negligible. A good quantitative agreement between experimental and numerical results was found within the explored range of Reynolds numbers. [Preview Abstract] |
Monday, November 19, 2007 4:01PM - 4:14PM |
JR.00003: Flow field expression in a superposition of dipole flows and identification of dipole moment by continuous wavelet transform Kazuyuki Ueno, Yuko Matsumoto Continuous wabelet transforms suitable for incompressible flows are discussed. Bessel type wavelet is introduced and inverse transform is extended so that the divergence-free condition of the flow field is automatically satisfied. This extension results in the flow field expression in superposition of dipole flow fields. An efficient way to substitute a set of dipoles for the flow field is proposed to reduce the computational cost. Applications of the present transform for several two-dimensional flows are shown. [Preview Abstract] |
Monday, November 19, 2007 4:14PM - 4:27PM |
JR.00004: Oscillating Dipolar Vortex Generated by Electromagnetic Stirring Aldo Figueroa, Sergio Cuevas, Eduardo Ramos The continuously driven laminar flow produced by an oscillating electromagnetic force in a thin electrolytic fluid layer is studied experimentally and numerically. The flow is generated by the interaction of an injected alternate electric current and a steady magnetic dipole field normal to the layer. Alternate currents with frequencies and amplitudes in the range of 10-50 mHz and 1-5 mA, respectively, are explored. The electromagnetic force stirs the fluid and produces an oscillating dipole vortex that enhances the fluid mixing. A numerical 2D solution of the full MHD equations that considers an analytical expression to model the non-uniform magnetic field is obtained. Numerical results show a good qualitative agreement with the experiments. Flow visualization and numerical particle tracking indicate that the mixing rate is increased although lateral transport seems to be inhibited due to symmetry conditions. [Preview Abstract] |
Monday, November 19, 2007 4:27PM - 4:40PM |
JR.00005: Chaotic advection in unstable two-dimensional circular vortices. Isabel Malico, Paulo Ferreira de Sousa Chaotic advection was studied in the formation process of multi-pole vortices that result from unstable monopole circular vortices. The unsteady, incompressible two-dimensional Navier--Stokes equations were solved with fourth-order Runge--Kutta temporal discretization and fourth-order compact schemes for spatial discretization. By examining patterns of the spatial variation of finite-time Lyapunov exponents, it is seen that as the initial perturbation to the flow grows, the resultant flow is dominated by chaotic regions that trap small regions of invariant tori. It is also seen that the regular regions surrounding the chaotic bands are the main barriers to the transport identified during the multi-pole formation. Lagrangian Coherent Structures (LCS) are also employed in this study, and their evolution is compared with the patterns of finite-time Lyapunov exponents. [Preview Abstract] |
Monday, November 19, 2007 4:40PM - 4:53PM |
JR.00006: Viscous interactions of asymmetric co-rotating vortex pairs Laura Brandt, Tomasz Cichocki, Keiko Nomura The physics underlying the interaction of a co-rotating vortex pair of equal size and different strengths in a viscous fluid is investigated. High resolution two-dimensional direct numerical simulations (DNS) are performed using a pseudospectral computational fluid dynamics code. The evolution of the vortices by diffusion and deformation are examined in the co-rotating frame. In the case of equal strength (symmetric) vortices, the vortices will merge through mutual core erosion and entrainment. The point at which the cores are entrained is marked by a critical aspect ratio (the vortex core radii over the separation distance). However, in the case of vortex pairs of different strengths (asymmetric), merger does not occur according to the criterion set by symmetric merger. The erosion and entrainment process is no longer mutual and a new merging criterion is developed based on the relative location of the central hyperbolic point with respect to each vortex. Depending on the relative strength of the two vortices, three flow regimes are possible: complete merger, partial merger and partial straining out. [Preview Abstract] |
Monday, November 19, 2007 4:53PM - 5:06PM |
JR.00007: Effect of ambient turbulence on the evolution of a counter-rotating vortex pair. Madiha Ahmed, Fazle Hussain In an attempt to explain and develop strategy for control of aircraft wake vortex in a turbulent atmosphere, the evolution of a vortex column dipole (a pair of counter-rotating vortices) in the presence of fine-scale (homogeneous and isotropic) freestream turbulence is studied via DNS of the Navier-Stokes equations. The freestream turbulence is found to significantly accelerate the vortex decay via a complex vortex-turbulence coupling scenario, which we study. External fine-scale turbulence is first stretched into azimuthal filaments (see also Melander {\&} Hussain, PRE, vol 48 (1993)) which merge into threads through successive pairings and advect along the column dipole by self-induction. Oppositely-directed advection of opposite-signed threads forms thread dipoles which then move outward by mutual-induction and also eject column fluid (see also J. S. Marshall, JFM, vol 345 (1997)). This has the effect of enhancing both mixing with the ambient fluid and the nominally planar reconnection (cross-diffusion) between the column vortex pair. We then further explore the column vortex dipole-turbulence interaction scenario and vortex decay dependence on parameters like the column vortex Reynolds number, separation of the vortices, and the intensity and scale of freestream turbulence. [Preview Abstract] |
Monday, November 19, 2007 5:06PM - 5:19PM |
JR.00008: Response Reconstruction for Traveling Wave Identification Harish Mukundan, Michael Triantafyllou, Franz Hover A large volume of research in vortex-induced vibration (VIV) is focused on elastically mounted rigid cylindrical bodies with much less attention given to flexible cylinders like risers. These risers may encounter a current with both magnitude and direction varying over the span. We consider the problem of obtaining and studying the VIV displacements (both cross-flow and inline) of such a riser along its entire length, when we are provided with some sensors measuring strains and accelerations. We will build the problem from the fundamental approach of using Fourier series, and evaluate criteria when such a reconstruction is allowed. The method will be applied to data from a set of experiments (uniform and linearly sheared profiles) conducted at Marintek wave basin. One feature observed from the experiments is the presence of traveling waves. Various methods for identifying traveling waves will be discussed. The mechanism of energy propagation and the interaction between CF and IL displacements during the process will be discussed. [Preview Abstract] |
Monday, November 19, 2007 5:19PM - 5:32PM |
JR.00009: Experiments in Methods of Vortex Induced Vibration Suppression Ricardo Galvao, Michael Triantafyllou, Franz Hover The suppression of vortex induced vibrations has many positive applications. A number of different structural modifications to a bare cylinder have been tested to determine their effect on vortex shedding and resulting vibrations. The effectiveness of these methods has been examined through imaging of the wake by means of Particle Image Velocimetry and a measurement of the drag force on the structure. A number of different configurations were considered. These include the attachment of an airfoil on opposing sides of the cylinder with and without the addition of a triangular backend. Another configuration considered involved the use of two pairs of airfoils of differing chord lengths attached at different positions relative to the cylinder. Degrees of freedom of these systems include angle of attack of the airfoils with respect to the freestream, height off of the cylinder and rotational angle of the airfoils about the circumference of the cylinder. Results show an overall improvement in reduction of the intensity of vortex induced vibrations with a drop in drag for specific combinations of airfoil position. [Preview Abstract] |
Monday, November 19, 2007 5:32PM - 5:45PM |
JR.00010: Calculation of complex singular solutions to the 3D incompressible Euler equations Michael Siegel We describe an approach for the construction of singular solutions to the 3D Euler equations for complex initial data. The approach is based on a numerical simulation of complex traveling wave solutions with imaginary wave speed, originally developed by Caflisch for axisymmetric flow with swirl. Here, we simplify and generalize this construction to calculate traveling wave solutions in a fully 3D (nonaxisymmetric) geometry. This is joint work with Russ Caflisch. [Preview Abstract] |
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