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 ER: Vortex Dynamics and 3D Vortex Flows III |
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Chair: F.J. Diez, Rutgers University Room: Salt Palace Convention Center 251 F |
Sunday, November 18, 2007 4:10PM - 4:23PM |
ER.00001: Structure of a low-momentum elevated jet in cross-flow. Stavros Tavoularis, Andrew Cameron, Matthew Johnson A complex flow field is generated in a water tunnel by discharging fully developed pipe flow into a uniform cross stream, well above the tunnel's boundary layer. The Reynolds number, based on the outer diameter of the pipe and the free stream velocity, ranged from 400 to 3000 and the ratio R of jet momentum flux to the cross-flow momentum ranged from 0.001 to 0.2, which correspond to the mixing-layer and backward-rolling vortex regimes. Flow visualization has identified the presence of four kinds of vortical structures: a K\'{a}rm\'{a}n vortex street, a large standing vortex near the pipe end, shear-ring vortices and tornado-like structures. The shear-ring structures are formed by Kelvin-Helmholtz instability of the nearly-elliptical mixing layer; as the momentum-flux ratio increases, their Strouhal number decreases in a non-linear fashion, with smaller structures merging to larger ones. Tornado-like structures form by stretching of the shear-ring structures; they appear only for 0.02 $<$ R $<$ 0.1, (mixing-layer regime) and seem to be active vortices. Quantitative studies are in progress to further investigate the nature of the tornado-like structures and the mechanisms of interaction among the different vortex kinds. [Preview Abstract] |
Sunday, November 18, 2007 4:23PM - 4:36PM |
ER.00002: Momentum Evolution of Ejected and Entrained Fluid During Laminar Vortex Ring Formation Paul S. Krueger, Ali B. Olcay Part of the complex flow evolution during vortex ring formation involves exchange of fluid momentum between ejected fluid, entrained fluid, and added mass. To investigate this process, vortex rings are generated numerically by transient jet ejection for fluid slug length -- to -- diameter (L/D) ratios of 0.5 -- 3.0 using three different velocity programs at a jet Reynolds number of 1000. Lagrangian coherent structure (LCS) techniques are utilized to identify ejected and entrained fluid boundaries, and a Runge-Kutta 4$^{th}$ order scheme is used for advecting these boundaries with numerical velocity data. By monitoring the center of mass of the fluid boundaries, momentum of the ejected and entrained fluid is calculated and related to the total impulse provided by the vortex ring generator. It is observed that most of the ejected fluid's momentum is transferred to the added mass while the jet is on for trapezoidal and triangular positive slope velocity programs. Also, as L/D is reduced from 3.0 to 1.0, momentum of entrained fluid in the formed ring is more than doubled. [Preview Abstract] |
Sunday, November 18, 2007 4:36PM - 4:49PM |
ER.00003: Vortex dynamics and entrainment mechanisms in lobed jets Ilinca Nastase, Amina Meslem Two isothermal turbulent air jets from lobed nozzles with inclined and respectively non inclined lobes and a circular reference jet with the same initial Reynolds number were experimentally studied. Quantitative image processing of time resolved visualizations as well as hot-wire measurements of the velocity spectra allowed an objective understanding of the vortex roll-up mechanisms. Unlike the circular jet, where the primary rings are continuous, the Kelvin-Helmholtz vortices in the lobed jet flows are discontinuous at the locations where the exit plane curvature turns to infinite. Primary structures detach at different frequencies whether they are shed in the lobe troughs or at the lobe sides. The ``cutting'' of the Kelvin-Helmholtz vortices enables the development of permanent secondary streamwise structures. Their momentum flux transport role is thus rendered more efficient and seems to be amplified by the double inclination of the injection boundary. The quantification of the entrained flow rates by means of LDA measurements perfectly agrees with these observations. [Preview Abstract] |
Sunday, November 18, 2007 4:49PM - 5:02PM |
ER.00004: Thrust Characterization for Vortex Ring Thrusters Mike Krieg, Kamran Mohseni Synthetic jets are zero net mass pulsatile jets that are commonly used in flow control applications in air. In these cases the natural resonant frequency of the actuators plays an important role. In this work we will present thrust characterization of vortex ring thrusters (VRTs) in liquid (equivalent of synthetic jets in liquid medium). VRTs design are motivated by pulsatile jet propulsion in squid and jellyfish. A prototype jet thruster was designed and build for this investigation. The effect of the actuation frequency and stroke ratio on the thrust level was experimentally studied. A simplified slug model was defined which predicted the thrust according to the momentum transfer. According to the model the thrust values for various frequencies converges to a single non-dimensionalized thrust, which is only a function of the stroke ratio. The accuracy of the model was defined in terms of a coefficient $\alpha $ which related predicted thrust values to those measured experimentally. This coefficient was observed to be nearly unity for stroke ratios below the formation number of the jet, and for frequencies below critical cavitation frequencies. $\alpha$ was seen to decrease (measured thrust drops below predicted thrust) with increasing frequency for all jets with stroke ratios above the formation number. The feasibility of using such a device in typical marine vehicles was tested by implementing the thruster in an unmanned underwater vehicle. The vehicle test-bed was operated in various dynamic maneuvers, including a simulated parallel park. [Preview Abstract] |
Sunday, November 18, 2007 5:02PM - 5:15PM |
ER.00005: Flow Visualization for Pulsatile Vortex Ring Thrusters Torin Clark, Kamran Mohseni Formation and evolution of vortex rings produced from pulsatile vortex ring thrusters were studied using flow visualization techniques. A vortex ring thruster consists of a cavity with an orifice at one end and an oscillating plunger at the opposite end which periodically creates a volume change in the cavity forcing a jet emission of fluid through the orifice into the surrounding reservoir. The ratio of the cylindrical jet length to its diameter, known as the stroke ratio, is a primary factor in the vortex ring formation characteristics. Flow visualization was employed in order to measure the translational velocity of the leading vortex ring for the range of stroke ratios of 2-7.5. It was observed that vortex rings with smaller stroke ratios have lower induction velocities, but the initial velocity is retained for a longer period of time as compared with vortex rings with larger stroke ratios. Additionally vortex ring dimensions, including semi-major axis, semi-minor axis, the ratio of these dimensions, and core to core radius, were considered. Also the volume of the vortex ring atmosphere was studied. The variations of these parameters with respect to Reynolds number, stroke ratio, time, and distance from the orifice are investigated. Finally the vortex ring formation and evolution during periodic operation of the vortex ring thrusters were visualized for various actuation frequency and stroke ratios. [Preview Abstract] |
Sunday, November 18, 2007 5:15PM - 5:28PM |
ER.00006: Vorticity dynamics and thrust during VRS Omer Savas, Richard Green, Francis Caradonna Under certain conditions of rapid descent of a rotorcraft, the vortices that usually trail below a rotor disk to form the helical vortex wake collapse into a ring-like structure around the plane of the disk, which is known as the vortex ring state (VRS). The formation and subsequent breakdown of the ring-like vortex is accompanied by large thrust excursions. In axial descent the thrust excursions are aperiodic, while in non-axial descent a periodicity on the order of several tens of rotor revolutions is observed. We discuss here experimental observations of the phase relation between the thrust cycle and vorticity distribution. The experiments were performed in a towing tank using a three-blade rotor. Rotor thrust was measured by strain gages and the vorticity fields using PIV. The flow structure as marked by vorticity distribution highlight the changes in the flow topology during the VRS cycles contrast the flow behavior at the leading and the trailing edges. The flow over the trailing edge exhibits large variations, whereas that over the leading edge is more tamed. Maxima of the VRS thrust oscillations correlate well with the maxima of enstrophy observed at the trailing edge of the rotor disk. [Preview Abstract] |
Sunday, November 18, 2007 5:28PM - 5:41PM |
ER.00007: 3D Particle Tracking Velocimetry Method for Lagrangian Measurement of Underwater Vortex Rings K.F. Washington, F.J. Diez Vortex Rings generated by an underwater speaker were studied using volumetric 3D Particle Tracking Velocimetry. Instantaneous visualization of the full structure of vortices can be difficult to obtain, but could give valuable insight into the behavior of unsteady vortices. Typically, measurements of an entire volume are difficult to obtain, and more often measurements at specific points or planes are obtained instead. In this study, the structure of vortices at various instances in time was obtained using a volumetric particle tracking velocimetry (PTV) method. The observation volume had dimensions of 40mm x 40mm x 40mm and a low density particle seeding of approximately 75 particles/cm3 was used. Four cameras were used to obtain all the information required to track the position of the seeding particles in the observed volume. The images from the four cameras were analyzed by a 3D PTV algorithm obtained through a collaboration with the group of Dr. Kinzelbach at the Swiss Federal Institute of Technology. Using this method, the three components of the velocity for each particle could be tracked as a function of time and used to aid in both the visualization and characterization of the 3D behavior of unsteady vortical flows. The 3D vortical structures were generated by an underwater speaker fitted with a converging nozzle. The system was operated at frequencies between 1-100Hz and was optimized for maximum thrust. [Preview Abstract] |
Sunday, November 18, 2007 5:41PM - 5:54PM |
ER.00008: The Stability and Evolution of a Family of $M = 2$ Uniform Vortices P. Luzzatto-Fegiz, C.H.K. Williamson Motivated by observations of merger of two corotating vortices, Cerretelli \& Williamson (2003) discovered a family of vortex patches representing the continuation of the uniform pair into a single `dumbbell' shape. This branch of solutions passes through a bifurcation from the Kirchhoff ellipses (found by Kamm 1987) and ends into a cat's eye shape. We compute the linear stability of the two-vortex configuration, with findings in agreement with Kamm (1987) and Dritschel (1995). Evolutions computed using contour surgery show that, while a pair of marginally unstable vortices remains roughly antisymmetric through the simulation (see Dritschel 1995), two strongly unstable vortices, after merging into a `dumbbell' shape, spontaneously exhibit symmetry breaking, leading to two structures of unequal size. Interestingly, we find that all the singly connected shapes are unstable to perturbations with wavenumber $m = 3$; indeed, simulations of `dumbbells' show a striking similarity with the case of the strongly unstable pair, again yielding symmetry breaking. Intrigued by the possibility of discovering bifurcated solution branches, we studied two cases where a change of stability coincides with an energy extremum, only to find that, as each zero eigenvalue is approached, the associated eigenmode reverts to a rotation of the vortex. As the shapes are invariant under rotation, both bifurcations are trivial, and thus do not yield new solution branches. [Preview Abstract] |
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