Bulletin of the American Physical Society
2005 58th Annual Meeting of the Division of Fluid Dynamics
Sunday–Tuesday, November 20–22, 2005; Chicago, IL
Session KG: Vortex Dynamics III |
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Chair: Thomas Corke, University of Notre Dame Room: Hilton Chicago Williford A |
Monday, November 21, 2005 4:10PM - 4:23PM |
KG.00001: Extension of the formation time concept to general planforms and trajectories Michele Milano, Mory Gharib We propose a generalization of the concept of formation time for flapping wings and appendages, that overcomes the drawbacks of Strouhal number and paves the way to the development of a unified theory for the unsteady aerodynamics of flapping propulsion. We show experimental evidence of the universality of the generalized formation time concept coming from results on flapping flat plates, shape optimization of flapping wings, and trajectory optimization for the caudal fin of an arrtificial fish. [Preview Abstract] |
Monday, November 21, 2005 4:23PM - 4:36PM |
KG.00002: LES investigation of aircraft wake two-vortex system in low level atmospheric turbulence Gregoire Winckelmans, Louis Dufresne, Laurent Bricteux The numerical simulation of realistic vortical aircraft wakes constitutes a challenging task, as the problem is of large size, the vortex cores are small, and the Reynolds number is very high. In particular, the vortex cores grow very little during the lifetime of the vortices. Large-eddy simulation (LES) at ``essentially'' infinite Reynolds number is here used: a Fourier-based pseudo-spectral method in ``quasi- Euler'' mode ($\nu$ set to zero and use of a high order $k^{16}$ hyperviscosity subgrid-scale model, which ensure negligible viscous core growth). The LES grid is also fine enough so as to properly capture relevant dynamics in the core region. A realistic case is simulated: circulation $\Gamma_0=400\,{\rm m} ^2/{\rm s}$, spacing $b_0=50\,{\rm m}$, core radius $r_c=2.5\, {\rm m}$. We use a $L^3$ computational box of $256^3$ grid points and with $L=200\,{\rm m}$. The background atmospheric turbulence is here at low level (dissipation $\epsilon = 0.0001\, {\rm m}^2/{\rm s}^3$) and was obtained as a pre-simulation. The vortex system engulfs the ambient turbulence, the non-linear interactions then amplify it and this eventually leads to a vortex pair where the surrounding turbulence is independent of the atmospheric background: the low level turbulence thus acts as a seed to create a ``turbulent vortex pair'' that then lives and decays on its own. We also observe significant axial velocities in the core region. Those results are further being used for simulations of LIDAR return signal. [Preview Abstract] |
Monday, November 21, 2005 4:36PM - 4:49PM |
KG.00003: Stochastic analysis of wing-tip vortex wandering in turbulent free streams. Sean Bailey, Stavros Tavoularis Instantaneous measurements of the local velocity vector and streamwise vorticity were performed in the tip vortex of a finite wing with a NACA-0012 profile and a rectangular tip at Re = 240000 and angle of attack of 5$^{o}$. Results are reported on six transverse planes downstream of the wing, in an unobstructed free stream with a turbulence intensity of 0.3{\%}, as well in grid-generated turbulence with intensities of 2.5{\%} and 5.0{\%}. It was found that, although vortex formation and mean trajectory were unaffected by the turbulence, time-averaged velocity statistics in the vortex core were strongly influenced by random lateral motion of the vortex, which increased with increasing turbulence intensity. Analysis of velocity signals identified instances when the vortex axis was on the same horizontal or vertical plane as the probe tip, which provided an estimate of the probability density function of the vortex axis position, found to be approximately Gaussian. Joint PDF of the measured velocity components perpendicular to the vortex axis indicated that the instantaneous peak tangential velocity decayed with increasing streamwise distance. [Preview Abstract] |
Monday, November 21, 2005 4:49PM - 5:02PM |
KG.00004: Corotating Vortex Formation, Merger, and Modification Jamey Jacob Experimental results from a combined wind tunnel and tow tank study on the evolution, interaction, and merger of two corotating trailing vortices are presented. In the current study, NACA 0012 airfoils positioned at positive and negative angles of attack are used to generate a corotating vortex pair. Measurements with a seven-hole probe are used to extract 3-D velocity and pressure fields in the tunnel while PIV is used in the tow tank to measure 2-D velocity fields in the vortex wake. The semi-span length is varied in the experiments to investigate the effects of initial separation on vortex formation and merger. Experimental information of the vortex motion is compared with theoretical predictions. Comparison shows that at larger initial separations, the motion of the vortex pair is well estimated from the 2-D analysis, while at smaller separations, the motion of the vortex pair cannot be well predicted from the results of the line vortex assumption. Effects in forcing vortex breakup using a virtual winglet from a plasma actuator are presented. At sufficient power inputs, the virtual winglet can substantially modify the vortex circulation magnitude and distribution. Comparisons of information confidence and data quality are made between the two measurement techniques and facilities. Finally, comparisons of differences in the vortex roll-up and evolution due to initial separation changes are discussed and contrasted to that of a single tip vortex and corotating vortex pair on a wing with flap. [Preview Abstract] |
Monday, November 21, 2005 5:02PM - 5:15PM |
KG.00005: 2D PIV of a pitching airfoil Melissa Green, Kamalluddien Parker, Julio Soria Two dimensional particle image velocimetry (PIV) experiments were performed at the midspan of a sinusoidally pitching NACA 0020 airfoil. Measurements were taken for a range of Strouhal numbers up to 0.4 and at various Reynolds numbers. In addition, the velocity field around the airfoil moving in quiescent flow was obtained. The flow is measured in a phase-averaged sense. Far field measurements of the surrounding flow field are presented in order to investigate the generation and propagation of the wake of the pitching motion. Near field measurements are also presented at the leading edge of the airfoil in order to resolve and investigate the behavior of the dynamics stall vortex and the shear layer. [Preview Abstract] |
Monday, November 21, 2005 5:15PM - 5:28PM |
KG.00006: Simulation of a 2D flow past a flexible fibre tethered at its center point: vortex shedding Luoding Zhu Vortex shedding from an object immersed in a flowing fluid is an important and interesting topic and has been extensively studied experimentally, analytically and computationally. Most of the work focused on vortex shedding from a rigid body; for instance, a circular cylinder [1], a sphere [2] or an inclined flat plate [3]. Here we report our simulation of vortex shedding from the two free ends of a flexible fibre with its center point tethered (otherwise unrestricted) in a two-dimensional flowing viscous incompressible fluid by the immersed boundary method [4]. The motivation of our work is a laboratory experiment reported in [5]. The Reynold numbers range from $2000$ to $40,000$ in the experiment and the authors focused on drag reduction caused by self-similar bending of the fibre. Our work concentrates on the vortex shedding at lower Reynolds numbers ($12.5-375$), investigating the influences of inflow speed, fibre length and fibre bending rigidity on the vortex shedding. \vskip 2mm {\underline {References}} \small \noindent [1] C.H.K. Williamson and R. Govardhan, {\it Annu. Rev. Fluid Mech.} {\bf 36}, 413 (2004). \noindent [2] S. Lee, {\it Computers \& Fluids} {\bf 29}, 639 (2000). \noindent [3] T. Sarpkaya, {\it J. Fluid Mech.} {\bf 68}, 109 (1975) \noindent [4] C.S. Peskin, {\it Acta Numerica} {\bf 11}, 479 (2002). \noindent [5] S. Alben, M. Shelley, and J. Zhang, {\it Nature} {\bf 420}, 479 (2002). [Preview Abstract] |
Monday, November 21, 2005 5:28PM - 5:41PM |
KG.00007: Vortex Shedding Dynamics in the Wake of Slender Cones at Low Reynolds Numbers Peter Monkewitz, Michel Provansal Since the original work of Gaster, the K\'{a}rm\'{a}n vortex shedding from slender cones placed normal to an oncoming uniform flow has been thought to lead to a series of stationary cells along the cone span, separated by zones of dislocations, with constant shedding frequency within each cell. Experiments on two cones with taper ratios of 3.2 10$^{-3}$ and 6.7 10$^{-3}$ are reported for local Reynolds numbers ranging between 40 and 180. By visualizing the plan view of the wake with hydrogen bubbles and determining local ``instantaneous'' frequencies, wave lengths and shedding angles from a digital movie, it is shown that shedding cells do appear but consistently move towards the thin end of the cone. An attempt is made to correlate this spanwise cell velocity with the speed of ``hole-solitons'' in the spanwise Ginzburg-Landau equation. Finally, it is shown why the data processing employed in previous studies can make moving cells look stationary. [Preview Abstract] |
Monday, November 21, 2005 5:41PM - 5:54PM |
KG.00008: Free-stream shear effects on vortex shedding from step-cylinders. Warren Dunn, Stavros Tavoularis In a recent experimental study we examined the complex process of vortex shedding from cylinders with a stepwise change in diameter inserted in uniform streams. The present work examines vortex shedding from a step-cylinder with a diameter ratio near 2 in uniformly sheared flow generated by a curved screen in a water channel. The Reynolds number, based on the centreline velocity and the large cylinder diameter, was in the range 268 to 622. The experimental techniques include laser Doppler velocimetry and flow visualization by electrolytic precipitation. Compared to the uniform flow case, vortices in the shear flow were generally less well-defined. In both the uniform and shear flows, spectra identified spanwise cells of constant frequency, including a distinct cell near the step, but the number of cells was larger in the shear flow case. The orientation of the cylinder axis relative to the shear direction affected the spanwise length of the near-step cell, the frequency difference between this cell and the adjacent cell behind the large cylinder, and the inclination of vortices behind both cylinders. Wavelet analysis showed that the vortex shedding frequency changed constantly with time near cell boundaries and within the near-step cell. [Preview Abstract] |
Monday, November 21, 2005 5:54PM - 6:07PM |
KG.00009: Instability of a junction vortex Takashi Naitoh, James Allen The flow field in the region where a moving wall, started from rest, slides under a stationary one, produces an interesting flow phenomena with relatively simple generation geometry. Experiments show that if the wall speed is high enough a vortex forms close to the junction of the moving wall with the stationary one. Vortex formation was observed for the range of Reynolds number $5 \times 10^2 \rightarrow 5 \times 10^5$, where the length scale is the distance the wall has moved from rest. The data reveals that in the absence of an apparatus length scale, the vortical structure appears to scale in a self- similar fashion that is consistent with the impulse provided by the moving wall. Over this Reynolds number range the vortical structure, which is initially laminar, begins to transition at $16 \times 10^3$ and appears to be turbulent by $40 \times 10^3$. The transitional regime is marked by the appearance of an instability wave on the perimeter of the vortical structure. The instability mechanism appears to be centrifugal in nature. The formation and non-linear growth of these structures and their ingestion into the primary vortex core is what causes the eventual breakdown of the primary vortex. [Preview Abstract] |
Monday, November 21, 2005 6:07PM - 6:20PM |
KG.00010: Fluidic-Driven Ducted Heat Ejector D. Gerty, R. Mahalingam, A. Glezer Unsteady, small-scale fluid mechanics and heat transport processes within a high-aspect ratio ducted heat ejector are investigated experimentally. The ducted heat ejector exploits the flow that is induced within the channel by the motion of a vibrating reed to cool the inner surfaces of the duct walls and thereby transport heat across its boundaries to cool electronic hardware by direct contact. This cooling approach is particularly attractive for low-power, densely-packed electronic hardware where heat is removed by direct conduction through the duct walls. The time harmonic motion of the reed results in the regular shedding of nominally two-dimensional counter-rotating vortical structures and induces a net flow through the duct. The flow characteristics are investigated using high-resolution particle image velocimetry (PIV). Of particular interest is the effect of the induced, small-scale motions and enhanced mixing on heat transfer across the duct boundaries which is comparable to conventional time-invariant channel flows at higher Reynolds numbers. [Preview Abstract] |
Monday, November 21, 2005 6:20PM - 6:33PM |
KG.00011: Starting jets of finite width and formation time of vortex dipoles Yakov Afanasyev Evolution of a two-dimensional flow induced by a jet ejected from a nozzle of finite size is studied experimentally. Vortex dipole forms at the front of the developing flow and then moves forward with constant speed. Trailing jet establishes behind the dipole. The dynamics of the flow is discussed on the basis of detailed measurements of vorticity and velocity fields which are obtained using particle image velocimetry. It is found that within the range of control parameters used in our experiments the dipoles never separate from the jet which is in contrast to the behavior of vortex rings reported previously by other authors. However, the formation time for the dipoles can be introduced such that after the formation the dipoles start moving away from the nozzle. Their dynamics after the formation is characterized by a reduced flux of vorticity from the jet. A value of the ratio of the speed of propagation of the dipole to the mean velocity of the jet is found to be 0.5 for later times of the evolution of the flow. A theoretical model is offered to predict quantitatively the initial propagation of the dipole as well as its steady-state regime. [Preview Abstract] |
Monday, November 21, 2005 6:33PM - 6:46PM |
KG.00012: Merging of unequal strength co-rotating vortices Louis Dufresne, Julien Christophe, Olivier Gourgue, Gregoire Winckelmans We present numerical simulation results on the 2D merging of a pair of co-rotating vortices and examine the effect of varying the circulation ratio between the two vortices. In a first step we present the results obtained for a pair of equal strength vortices ($\Gamma_2/\Gamma_1 = 1$) at a Reynolds number of $\mathit{Re} = \Gamma_1/\nu = 530$. A detailed quantitative analysis is made and shown to be in very good agreement with the experimental measurements of Cerretelli \& Williamson (2003, JFM, {\bf 475}, 41--77) for that same case. The results for vortex pairs with unequal strengths, i.e.\ with $\Gamma_2/\Gamma_1 < 1$, also at $\mathit{Re} = 530$, are presented next. The decomposition of the vorticity field into its symmetric and anti-symmetric components, as done by Cerretelli \& Williamson, shows that the structure of the anti-symmetric vorticity, in the convective merging phase, completely changes when $\Gamma_2/\Gamma_1$ reaches a value of about 0.8. Above that value, both vortices undergo deformation and contribute to the apparition of anti-symmetric vorticity. They also both move towards the center of rotation while they merge. Below that value, only the weaker vortex undergoes significant deformation and thus contributes to the apparition of anti-symmetric vorticity. Furthermore, the center of that weak vortex remains almost stationary (in the proper rotating frame of reference). The stronger vortex follows the opposite behavior with only a little deformation but with a more significant relative displacement. [Preview Abstract] |
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