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 L18: Vortex Dynamics: Vortex Rings |
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Chair: Megan Leftwich, George Washington University Room: 2004 |
Monday, November 24, 2014 3:35PM - 3:48PM |
L18.00001: On Axisymmetry of Vortex Rings Ahmad Falahatpisheh, Arash Kheradvar The shape of vortex rings can be an indication of the axisymmetry of propulsion or transient jet flows. There are many conditions that vortex rings deviate from axisymmetry. For the first time, we introduce a metric, called axisymmetry index, $\xi$, that measures the axisymmetry of vortex rings with a single value. Axisymmetry index examines the spectrum of the impulse of the ring in azimuthal planes and reports the degree by which the ring deviates from axisymmetry. The index is systematically investigated in analytical and numerical cases. A perfect axisymmetric ring is associated with $\xi=1$. It is validated in Gaussian vortex ring and Hill's spherical vortex, where the computed indices are found to be in agreement with $\xi=1$. A family of non-axisymmetric vortex rings are parametrically generated to study the relation of the index with the ratio of the maximum of circulation to the minimum of circulation of the ring. The results show that as the second moment of vorticity on one side increases compared to the other side, the deviation of the ring from axisymmetry increases, hence, a decrease in the index from unity. We also present results of numerically investigating the axisymmetry of a non-axisymmetric vortex ring that forms downstream of an oval-shaped nozzle. [Preview Abstract] |
Monday, November 24, 2014 3:48PM - 4:01PM |
L18.00002: On the vortex ring state Richard Green, E. Gillies, M. Giuni, J. Hislop, Omer Savas The investigation considers the vortex ring state, a phenomenon normally associated with the collapse of a trailing, helical vortex wake into a unstable vortex ring, and is a problem encountered when a helicopter rotor descends into its own wake. A series of wind tunnel and towing tank experiments on rotor systems have been performed, and a comparison is then made with the behaviour of a specially designed open core, annular jet system that generates a mean flow velocity profile similar to that observed below a rotor. In experimentally simulated descents the jet system forms flow patterns that are topologically similar to the vortex ring state of a rotor system. Furthermore the dynamic behaviour of the flow shares many of the important characteristics of the rotor flow. This result suggests that the phenomenon of the vortex ring state of a rotor wake is decoupled from the detailed vortex dynamics of the helical vortex filaments themselves. The presentation will describe the principle behind the investigation, the details of the annular jet system and the results gained using PIV and flow visualisation of the wake and jet systems. [Preview Abstract] |
Monday, November 24, 2014 4:01PM - 4:14PM |
L18.00003: Pressure drag evolution of a pair of interacting vortex rings Angeliki Laskari, Rammah Shami, Roeland de Kat, Bharathram Ganapathisubramani To determine whether there is a drag benefit for interacting vortex rings compared with a single one, we obtain time evolution of pressure drag coefficients of a pair of interacting vortex rings using 2D Particle Image Velocimetry data. Finite-Time Lyapunov Exponent fields are used to identify vortex boundaries. Streamwise pressure gradients are computed using the incompressible Navier Stokes equations and subsequently integrated across the boundary of the rings. The acceleration term is estimated by either an Eulerian, Lagrangian or Taylor's Hypothesis approach. Preliminary results show that the latter appears to be the least sensitive to noise, resulting in smoother acceleration fields and fewer oscillations in the evolution of the pressure drag coefficient. Effects of different separation lengths are assessed for the interacting pair and results are compared with those for a single ring. [Preview Abstract] |
Monday, November 24, 2014 4:14PM - 4:27PM |
L18.00004: A Pressure-Based Analysis of Vortex Ring Pinch-Off Kristy Schlueter, Noah Braun, John Dabiri This study investigated the development of vortex rings over a range of maximum stroke ratios, and analyzed vorticity and pressure data for clues to the physical mechanisms underlying vortex pinch-off. An impulsive piston velocity profile and Reynolds number of 3000 were used for all cases. The formation number was consistently found to be 3.6 +/- 0.3. A recently developed algorithm was used to generate pressure fields by integrating the pressure gradient along several paths through the velocity field and taking the median to get explicit values for pressure. The formation time at the occurrence of a local maximum in the pressure between the vortex ring and the lip of the nozzle, known as the trailing pressure maximum, was found to occur concurrently with the formation number for each case, within the error associated with the temporal resolution of the data. This suggests that the trailing pressure maximum is an indicator of vortex ring pinch-off. This is consistent with the results of Lawson and Dawson (2014), who found that the appearance of the trailing pressure maximum was coincident with the formation number. This pressure based approach to determining vortex ring pinch-off will be applied to a biological flow to examine the efficiency of such a flow. [Preview Abstract] |
Monday, November 24, 2014 4:27PM - 4:40PM |
L18.00005: Entrainment in interacting vortex rings Rammah Shami, Bharathram Ganapathisubramani The efficiency of entrainment in single vortex rings has been examined by various studies in the literature. These studies have shown that this efficiency is greatly increased for smaller stroke-time to nozzle-diameter ratios, L/D. However, no clear consensus exists regarding the effect on the entrainment process for the sectioned delivery of the vortex forming impulse. In the present work the entrainment mechanism associated with the interaction between two co-axially separated vortex rings is explored. Planar, time-resolved particle image velocimetry (PIV) measurements are taken of a interacting vortex flow field. Lagrangian coherent structures (LCS) extracted from the finite-time Lyapunov exponent (FTLE) fields are employed to determine the vortex boundaries of the interacting rings and is then used to measure entrainment. Preliminary results indicate that whilst the most efficient entrainment of ambient fluid by the ring pairs occurs at larger separations, the rate and overall mass transport increase can be controlled by altering the spatial/temporal separation between successive rings and is higher at smaller ring spacing. Variation in mass transport behaviour for different ring strengths (L/D) and Reynolds numbers will also be discussed. [Preview Abstract] |
Monday, November 24, 2014 4:40PM - 4:53PM |
L18.00006: Numerical Study of the Formation and Interaction of Concentric Vortex Rings Vahid Sadri, Paul S. Krueger Transient flow between concentric cylinders produces concentric opposite signed vortex rings, which exhibit a range of interesting behavior. Concentric vortex--ring interaction was studied numerically to determine the effects of cylinder gap ratio ($\Delta $D/D) and jet stroke length-to-gap ratio (L/$\Delta $D) on the evolution of the vorticity and the trajectories of the resulting vortex pair. The flow was simulated at a jet Reynolds number of 2,000, L/$\Delta $D in the range 1--15, and $\Delta $D/D in the range 0.05--0.25. The results showed that the position of the vortices relative to each other during the formation phase played an important role in the trajectories of the vorticity centroids at later time. In particular, the vortex pair did not separate during the simulation period when the gap size was less than 0.1 and L/$\Delta $D was larger than 5. In the case that $\Delta $D/D was smaller than 0.1 and L/$\Delta $D was less than 5, the stopping vortices disturbed the orientation of the vortex pair and affected the evolution of the flow at later time. The general behavior of the vortex trajectories was categorized with respect to the generator parameters (L/$\Delta $D, $\Delta $D/D). [Preview Abstract] |
Monday, November 24, 2014 4:53PM - 5:06PM |
L18.00007: Impact of a vortex ring on a conical wall Sergio Hernandez Zapata, Erick Javier Lopez Sanchez, Gerardo Ruiz Chavarria In this work we present a numerical and experimental research of a vortex ring impinging a cone. Both the vortex and the conical wall have the same axis of symmetry. For this study we solve the Navier-Stokes and continuity equations in cylindrical coordinates using a finite difference scheme for r, z and time, whereas a Fourier spectral method is used for the angular variable. As initial conditions we assume that velocity is given by the Biot-Savart law for a vorticity distribution of constant magnitude inside a torus. With respect the experiments, measurements of velocity were made with a hot wire anemometer. To have a mapping in space we use a traverse system to place the hot wire probe in points of a grid. Additionally, the measurements of velocity are synchronized with the production of the vortex. Unlike the case of the impact with a flat wall, in this case the diameter of the vortex ring cannot grow. We study the shape of the vortex before the impact, the instabilities and the production of secondary vorticity during the impact. Finally, we made a comparison between experiment and the numerical simulations. [Preview Abstract] |
Monday, November 24, 2014 5:06PM - 5:19PM |
L18.00008: Vortex Ring Induced Mixing in a ``Step'' Stratification Jason Olsthoorn, Stuart dalziel The dynamics of fully developed turbulence in a density stratified fluid is highly complex. The highly unstable nature of stratified turbulence and its large range of length scales impede the analysis of the mixing of the density field. In the present work, we consider the mixing induced by coherent vortex rings. Vortex rings provide a reproducible source of kinetic energy and vorticity and have a well defined length scale. By measuring the mixing induced by the isolated mixing events as a result of a vortex ring interacting with a density stratification, we hope to shed insight into stratified turbulent mixing. We initialize a stable density stratification of two different density salt-water layers with a sharp pycnocline between them. We generate vortex rings in the less dense upper layer, and allow these rings to propagate into the more dense lower layer. The result is a pycnocline disturbance which mixes the fluid. Analyzing the change in potential energy of the fluid over multiple vortex ring/pycnocline interactions, we determine that after an initial setup period, the Richardson number dependence of the mixing is balanced by the change in pycnocline height resulting in a constant mixing rate. We present the analysis of the experimental work and discuss its implications. [Preview Abstract] |
Monday, November 24, 2014 5:19PM - 5:32PM |
L18.00009: A numerical study of a vortex ring impacting a permeable wall Jing Lou, Ming Cheng, T.T. Lim We numerically simulate a vortex ring impacting a permeable wall by using a lattice Boltzmann method. The study is on vortex ring/permeable wall interaction and to address some of the unanswered questions, including core vorticity, kinetic energy and enstrophy of the flow field. The simulation was conducted for a range of parameters such as wall open-area ratios, structure dimensions, wall-thicknesses ( and Reynolds numbers. Results show that with increasing $\phi$ or $Re_\Gamma$ enhances vorticity transport across the permeable wall, leading to the formation of a regenerated vortex ring, whilst increasing $H$ impedes vorticity transportation and the formation of regenerated vortex ring. Moreover, higher $A$ promotes vortex shedding from the wire grids and generates fine-scale structures in the wake. [Preview Abstract] |
Monday, November 24, 2014 5:32PM - 5:45PM |
L18.00010: Buoyant Norbury's vortex rings Mark Blyth, Javier Rodriguez-Rodriguez, Hayder Salman Norbury's vortices are a one-parameter family of axisymmetric vortex rings that are exact solutions to the Euler equations. Due to their relative simplicity, they are extensively used to model the behavior of real vortex rings found in experiments and in Nature. In this work, we extend the original formulation of the problem to include buoyancy effects for the case where the fluid that lies within the vortex has a different density to that of the ambient. In this modified formulation, buoyancy effects enter the problem through the baroclinic term of the vorticity equation. This permits an efficient numerical solution of the governing equation of motion in terms of a vortex contour method that tracks the evolution of the boundary of the vortex. Finally, we compare our numerical results with the theoretical analysis of the short-time evolution of a buoyant vortex. Funded by the Spanish Ministry of Economy and Competitiveness through grant DPI2011-28356-C03-02 and by the London Mathematical Society. [Preview Abstract] |
Monday, November 24, 2014 5:45PM - 5:58PM |
L18.00011: Numerical investigation of vortex ring formation through a moving valve Lucas Farrar, Xudong Zheng, Qian Xue Impulsively started, low-speed, incompressible jets observed in nature, are commonly found as starting flows through a moving valve. Similar flows are found the human heart where blood is transported from the left atrium, through the mitral valve, and into the left ventricle. During this process, a vortex is formed around the lip of the moving valve before propagating into the left ventricle. We use numerical simulations to investigate the vortex dynamics of starting flows through an axisymmetric nozzle with time varying exit geometry. Following the experimental work of Dabiri {\&} Gharib (J. Fluid Mech., 2005, vol. 538, pp. 111-136), volumetric flow rate is held constant at the nozzle inlet, while the nozzle is treated as a rigid body with motion independent of fluid forces. We show that nozzle motion affects both vortex formation time and pinch-off time as well as the circulation and energy associated with the leading vortex ring. By parametrically ranging over a variety of prescribed flow rates and exit diameter frequencies, the independent contributions of the nozzle motion to the developing vortex structure are assessed. [Preview Abstract] |
Monday, November 24, 2014 5:58PM - 6:11PM |
L18.00012: Vortex rings in non-Newtonian viscoelastic fluids play yo-yo Julie Albagnac, David Laupsien, Dominique Anne-Archard Vortex rings are coherent vortical structures widely presents in geophysical flows and engineering applications. Numerous applications imply industrial processes including food processing, or petrol industry. Those applications are very often confronted with non-Newtonian fluids. Nevertheless, to the best of our knowledge, only few studies dealing with vortex dynamics in non-Newtonian shear-thinning fluids exist, and none with viscoelastic ones. The aim for the present study is to characterize experimentally the dynamics of vortex rings generated thanks to a piston-cylinder apparatus in various viscoelastic fluids as a function of the generalized Reynolds number, the piston stroke and the final piston position relative to the cylinder exit. In particular, the elastic property of the fluid will be highlighted by the furling-unfurling of vortex rings. [Preview Abstract] |
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