Bulletin of the American Physical Society
62nd Annual Meeting of the APS Division of Fluid Dynamics
Volume 54, Number 19
Sunday–Tuesday, November 22–24, 2009; Minneapolis, Minnesota
Session AT: Vortex Dynamics and Vortex Flows I |
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Chair: Jeffrey Marshall, University of Vermont Room: 200H |
Sunday, November 22, 2009 8:00AM - 8:13AM |
AT.00001: Harvesting energy in the wake of a circular cylinder using piezoelectric materials Dogus H. Akaydin, Niell Elvin, Yiannis Andreopoulos The voltage generated by short, flexible piezoelectric cantilever beams placed inside turbulent wakes of circular cylinders at Reynolds numbers of 10,000 is investigated experimentally and computationally. The coherent vortical structures present in this flow generate a periodic forcing on the beam which when tuned to its resonant frequency produces maximum output voltage. There are two mechanisms which contribute to the driving forcing of the beam. The first mechanism is the impingement of induced flow by the passing vortices on one side of the beam and second is the low pressure core region of the vortices which is present at the opposite side of the beam. The sequence of these two mechanisms combined with the resonating conditions of the beam generated maximum energy output which was also found to vary with the location in the wake. The maximum power output was measured at about two diameters downstream of the cylinder. This power drops off the center line of the wake and decays with downstream distance as (x/D)$^{-3/2}$. A three-way coupled interaction simulation that takes into account the aerodynamics, structural vibration and electrical response of the piezoelectric generator has been developed. [Preview Abstract] |
Sunday, November 22, 2009 8:13AM - 8:26AM |
AT.00002: Integrability and Chaos in Body-Vortex Interactions Johan Roenby, Hassan Aref We explore the class of dynamical systems consisting of a rigid body and $N$ point vortices in an ideal, unbounded, 2D fluid. The body is represented by a closed curve and is free to move in response to the fluid motion. It may have a prescribed circulation about it, which is conserved. The vortices have fixed strengths and are intended to model vortices that have been shed by the body or elsewhere in the flow field. The flow at any given time and position is determined by the instantaneous vortex and body positions together with the instantaneous linear and angular velocity of the body. The equations of motion may be cast in Hamiltonian form. We analyze the equations of motion using techniques from the theory of dynamical systems. The simplest such system, a single point vortex and a circular body, is integrable. As we add vortices, or change other features of the system such as the body shape, the motion may become chaotic. Numerical solutions are shown and analyzed with an emphasis on the transition to chaos and its physical meaning. This class of systems provides a rich family of few-degree-of-freedom systems that capture essential fluid-body interaction physics. [Preview Abstract] |
Sunday, November 22, 2009 8:26AM - 8:39AM |
AT.00003: Vortex suppression in the wake of counter rotating cylinders Peter Dewey, Alexander J. Smits Digital particle image velocimetry is used to study the flow past a pair of counter rotating cylinders placed side-by-side normal to the freestream flow direction. The Reynolds numbers based on cylinder diameter is varied from 100 to 200 and gap-to-diameter ratios of 1, 3 and 5 are considered. An unsteady wake consisting of a pair of von K\'{a}rm\'{a}n vortex streets is present in the flow field when the cylinders are rotated below a critical value. Above this critical value, counter rotation of the cylinders suppresses vortex formation. The critical rotational speed varies only slightly with Reynolds number but exhibits a strong dependence on the gap-to-diameter ratio. As the gap-to-diameter ratio increases, the critical rotational speed approaches values expected to suppress vortex formation for a single rotating cylinder, indicating that the wakes of the cylinder pair have more interaction for small gap-to-diameter ratios. At sufficiently high rotational speeds the streamlines around the cylinder pair resemble a doublet potential flow. The experiments were inspired by the computations performed by Andy Chan and Antony Jameson at Stanford University. [Preview Abstract] |
Sunday, November 22, 2009 8:39AM - 8:52AM |
AT.00004: Flow Development over a Circular Cylinder with a Stepwise Discontinuity Chris Morton, Serhiy Yarusevych Cross-flow around a step cylinder is common in various engineering applications, for example, heat exchangers and buildings, where understanding flow development is often of critical importance for engineering design. Moreover, the relatively simple geometry of a step cylinder allows modeling complex vortex interactions. For a step cylinder in uniform flow, the flow development is dependent on the Reynolds number (Re$_{D})$ and the ratio of the large cylinder diameter (D) to the small cylinder diameter (d). In this study, vortex shedding phenomena occurring in the wake of a step cylinder is investigated using an unsteady RANS based numerical approach for Re$_{D}$ = 300 and D/d = 2. Based on the numerical results, three distinct spanwise vortex cells were identified in the step cylinder wake: one vortex shedding cell in the wake of the small cylinder and two vortex shedding cells in the wake of the large cylinder. A comparative analysis with available experimental data showed that the numerical simulations adequately modeled wake vortex development and interactions in the near wake region. One of the vortex cells forming downstream of the step was found to have a cyclic appearance, with the periodicity being linked to downwash fluctuations near the step. In addition, the results suggest that streamwise vortices develop at the step and unsteady interactions between the streamwise and spanwise vortices occur in the near wake. [Preview Abstract] |
Sunday, November 22, 2009 8:52AM - 9:05AM |
AT.00005: Three dimensional flow around a flexible circular cylinder in cross-flow Francisco Huera-Huarte, David Jeon, Morteza Gharib The three dimensional flow around a flexible cantilever model undergoing vortex-induced vibrations has been studied by using Defocusing Digital Particle Image Velocimetry (DDPIV). The DDPIV technique allowed the simultaneous measurement of the motion and the flow around a portion of the cylinder. Different circular cylinder models accounted for several high aspect (length over diameter) and low mass ratios (mass over mass of displaced fluid), leading to flow-induced vibrations with different dominant mode shapes and frequencies. The quantitative study of the wake structures of cylinders able to vibrate at different structural modes is of particular interest as there is a lack of published results. Moreover, the mechanisms yielding to mode locked-on behavior and the topology of the wake under this situation are poorly understood. [Preview Abstract] |
Sunday, November 22, 2009 9:05AM - 9:18AM |
AT.00006: Vortex-Body Interaction using a Level-Set Based Overset Grid Method Simtha Renjitham, Jeffrey Marshall An overset grid method is presented for solution of the integral vorticity-velocity formulation of the Navier-Stokes equations. The method uses an inner body-fitted grid and an outer Cartesian grid. The Biot-Savart integral is solved using an adaptive, optimized multipole acceleration method. The integration is performed over all inner grid cells, over all ``active cells'' of the outer grid that lie entirely outside of the inner grid, and over sub-elements of a set of overhanging cells of the outer grid that overlap part of the inner grid. A level-set function is introduced in which the zero level-set curve coincides with the outer surface of the inner grid. This level-set function is used to rapidly subdivide the overhanging grid cells into triangular sub-cells which lie entirely outside of the inner grid, while omitting the parts of these cells that lie inside the inner grid, so as to avoid double-counting the vorticity in these regions. The pressure is solved as a post-processing variable using a boundary-element formation that requires evaluation of an integral using a parallel method to that used for velocity calculation. The method is applied to two-dimensional flow past stationary and moving bodies, and it is well suited to vortex-body interaction with complex, moving bodies. [Preview Abstract] |
Sunday, November 22, 2009 9:18AM - 9:31AM |
AT.00007: On the frequency of high Reynolds number shedding in bluff-body wakes Fernando Ponta In this talk we shall explore the physical phenomenon of vortex shedding at high and extra-high Reynolds number. We start from a previous work where Ponta and Aref introduced a rationale for the empirically observed Strouhal-Reynolds number relationship for vortex shedding at low Reynolds. Analyzing the turbulent transport of momentum, the rationale is extended to high Reynolds number regimes. Results compared satisfactorily with the existent experimental evidence, and their extension to extra-high- Reynolds geophysical flows will be discussed. [Preview Abstract] |
Sunday, November 22, 2009 9:31AM - 9:44AM |
AT.00008: Using a hybrid cyber-physical system in the study of body motion due to vortex dynamics A. Mackowski, C.H.K. Williamson We are interested in the effect of vortex dynamics causing vibration of bodies in a flow. In these studies, one needs to select essential parameters for the body, such as mass, spring stiffness, and damping. Normally, these parameters are set physically by selecting mechanical elements. However, in our approach, which utilizes a computer-controlled XY$\Theta$ towing tank and a force-feedback control system, we impose mass- spring-damping parameters in virtual space and in three degrees of freedom. [A similar concept, in one degree of freedom, was pioneered by a group at MIT (Miller 1996; Hover, Techet, Triantafyllou 1997), in studies of vortex-induced vibration of cables.] Although the use of a cyber-physical system has clear advantages over using a fixed, physical experiment, there are serious challenges to overcome in the design of the governing control system. The presence of noise in the dynamic force measurements and the effects of a finite time delay in controller response cause problems both for the implementation and physical accuracy of such a setup. In this presentation, we explore a new methodology for creating a controller suitable for systems with several degrees of freedom. Our controller, based on a discretization of Newton's laws, makes it straightforward to add and modify any kind of nonlinear, time-varying, or directional force, virtually. We shall present applications of this approach to problems in flow-induced vibration. [Preview Abstract] |
Sunday, November 22, 2009 9:44AM - 9:57AM |
AT.00009: Vortex-induced vibrations of an elastically mounted sphere at Re = 300: Hysteresis and vortex shedding modes Suresh Behara, Iman Borazjani, Fotis Sotiropoulos We carry out fluid-structure interaction (FSI) simulations to investigate the excitation mechanisms and vortex shedding modes of an elastically mounted sphere that is free to oscillate in all three directions using the FSI-CURVIB method [Borazjani et al, J. Comp. Physics, 2008]. The simulations are performed for Re=300 over a range of reduced velocities. We report novel results showing hysteresis in the response curve depending on whether the reduced velocity is decreased or increased. Large amplitude oscillations are found to persist even for small reduced velocities when the reduced velocity is decreased from higher values. Increasing the reduced velocity from low values, on the other hand, causes the large-amplitude oscillations to be excited only at higher reduced velocities. Our simulations elucidate the 3D wake structures associated with each hysteresis branch and reveal a new vortex shedding mode. We show that the lower hysteresis branch exhibits the standard braided-hairpin wake mode while the upper branch exhibits a striking wake structure characterized by intertwined, longitudinal spiral vortices. [Preview Abstract] |
Sunday, November 22, 2009 9:57AM - 10:10AM |
AT.00010: Vortex shedding interactions with an oscillating flat plate Arnold Song, Kenneth Breuer We present results from a model system designed to study the interactions between vortex shedding and structural compliance, as might be exhibited in systems as diverse as flying animals with compliant wings or traffic signs subject to hurricane-force winds. A sharp-edged plate is mounted at high angle of attack such that vortex shedding from the leading and trailing edges results in fluctuations of the aerodynamic forces. In its open-loop mode of operation, the angle of the plate is oscillated in a controlled sinusoidal manner, and the aerodynamic forces and vortex characteristics are measured using a torque sensor at the root of the support rod and a hot wire located in the wake. The onset of hysteresis in the aerodynamic forces generated during the pitching cycle is documented as a function of mean and fluctuating angles. In its closed-loop mode, the angle of the plate becomes a function of the aerodynamic forces such that an arbitrary virtual stiffness and damping can be proscribed. These different modes of operation, generated by the interactions between the fluid and structural forces are presented and discussed. [Preview Abstract] |
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