Session BU: Vortex Flows II

Vortex induced motion in compliant structures

The coupling of the unsteady shedding of vortices from the leading and trailing edges of a flat plate can lead to large scale oscillations of a structure. Examples of these large motions abound in engineered structures (Traffic signs vibrating in the wind, wing flutter, chattering venetian blinds, etc.) and in nature (the rustling of leaves on a tree in the wind). In all of these examples, the efficiency of energy extraction from the flow to the structure increases dramatically as the vortex shedding and structural vibrations near resonance. As the motion becomes more exaggerated, the fluid-structure interaction becomes increasingly nonlinear as the motion of the plate becomes increasingly important to the vortex shedding dynamics. We present experimental results from two related systems tested in a low speed wind tunnel (using high-speed videography, PIV and hotwire anemometry) (i) a rectangular cantilevered flat plate free to bend and twist, and (ii) a flexible ribbon pinned at its two ends and exposed to the flow. In both systems, a rich phase map of vortex-induced vibrations is described in which both mechanisms for vortex shedding and structural vibration can be tuned independently using geometry, material properties and flow conditions.   

Hydrodynamics of a Contracting Cylinder in Translation

The present study examines the effects of body contraction on the hydrodynamics of a circular cylinder shortly after it is subjected to an impulsive start. Results for the development of the fluid vorticity, hydrodynamic impulse and drag were obtained using computational fluid dynamics and a transient re-meshing scheme that allowed accurate computation of the viscous layers in the vicinity of the cylinder surface. Computational results were obtained for Re = (Ua/$\nu )$ = 9500, and a constant cylinder diameter, up to t* = tU/a = 6; U is the cross flow velocity and ``a'' is the cylinder radius. In this case the drag force increased with time and exhibited undulations that were correlated with vortex shedding events. Computations for a contracting cylinder were initiated at t* = 3.6 using average contraction rates of r = (da/dt)/U = -0.38 and -0.50. These revealed a symmetric but very complex vortex shedding pattern. The drag force on the gradually contracting cylinder decreased initially and then oscillated about zero. For the more rapid contraction the cylinder experienced a strong thrust, due to the hydrodynamic impulse of the shed vorticity, before tapering off.   

The three-dimensional wake of a swimming cylinder

Previous two--dimensional numerical studies have shown that a circular cylinder undergoing both oscillatory rotational and translational motion can generate thrust so that it actually self--propels through a stationary fluid. The current research reported here extends that study both experimentally and numerically, recording detailed vorticity fields in the wake and using these to elucidate the underlying physics, examining the development wake three--dimensionality experimentally, and determining the stability of the wake to the growth of three--dimensional flow through Floquet stability analysis. In particular, we find that the wake undergoes three--dimensional transition at low Reynolds numbers to a instability mode with a wavelength of about two cylinder diameters. The stability analysis indicates that the base flow is also unstable to another mode at slightly higher Reynolds numbers, broadly analogous to the three-dimensional wake transition for a circular cylinder despite the distinct differences in wake/mode topology. The three-dimensional transition leads to significant changes to the mean two-dimensional base flow, and the effect on the forces on the cylinder are currently under investigation.   

Vortex Dynamics Around a Bottom-Mounted, Short Cylinder in Oscillatory Flow

In coastal environments, the interaction of the reversing flow field with a stationary object is governed by complex vortex dynamics. For obstacles bounded by the sea bed, the locally generated and ejected vortices play a significant role in the scour and burial of these obstacles. In this research, the vortex dynamics around a short, bottom-mounted cylinder in oscillatory flow and the resulting time-dependent forcing at the bed are investigated with detailed numerical simulations performed with the commercially available model, FLOW-3D, utilizing a Large Eddy Simulation (LES) turbulence closure scheme. Model predictions of the magnitude, location, and shape of the centerline vortical structures were in good agreement with available laboratory data. During the wave half period, two vortex structures are identified: the upstream horseshoe vortex and the downstream arch vortex. As the flow reverses, the upstream horseshoe vortex advects away from the cylinder and dissipates, while the lee arch vortex flips over the top of the cylinder. In regular waves, this process is mirrored and repeated every half wave period. Two Keulegan-Carpenter number dependent vortex flipping regimes were observed: the single-vortex mode and the two-vortex mode. Ongoing investigations will examine the impact of these vortex dynamics on the applied bed shear.   

Axial Vorticity in the Wake of an Inclined Slender Body

The generation and evolution of axial vorticity in the wake of an inclined slender body is studied using 2D Particle Image Velocimetry (PIV) measurements around a 6:1 Prolate Spheroid mounted at a 10\r{ } angle of attack in a hydraulic flow channel. Long time series measurements of PIV data at Reynolds numbers (Re$_{L}$=UL/$\nu )$ of 0.15, 0.3, and 0.5x10$^{6}$ in planes normal to the flow were obtained at several stations along the body and at downstream distances up to one body length. This is an extension into the wake region of a number of previous numerical and experimental studies on vortex roll-up on the body of a 6:1 Prolate Spheroid (for example Fu \textit{et al} (1994), Tsai and Whitney (1999)), where the emphasis was on characterizing the vortex structure near the body and the related lift coefficients. In the present study the focus is on the structure of the axial vorticity present in the wake downstream of the body, both instantaneously and in the mean. In the mean, it is found that the primary axial vorticity is generated in reaction to the lift but an additional source of vorticity is due to the interaction of the primary vorticity with the tail of the hull, resulting in two oppositely oriented vortex-tube pairs. Instantaneously, the primary and secondary vortex tubes are comprised of multiple smaller vortex tubes rather than larger, more well defined tubes evident in the mean.   

Meander of a Fin Trailing Vortex Measured using Particle Image Velocimetry

The trailing vortex shed from a tapered fin installed on a wind tunnel wall was studied using stereoscopic particle image velocimetry in the crossplane to investigate the low-frequency meander of the vortex, with data acquired at several locations downstream of the fin trailing edge for multiple fin angles of attack at Mach 0.8. Analysis shows that the meander amplitude increases with downstream distance and decreases with vortex strength, consistent with previous studies indicating that meander is induced by an influence external to the vortex itself. Instantaneous vector fields reveal that the turbulence originating in the boundary layer on the nearby wind tunnel wall is lifted and drawn towards the vortex core, suggesting that this wall turbulence may contribute to the vortex meander. This was confirmed by energizing the incoming boundary layer using low-profile vortex generators and observing a substantial increase in the meander amplitude. These results demonstrate that for low-aspect-ratio lifting surfaces in proximity to a wall, such as missile fins, vortex meander results from the wall boundary layer turbulence as well as known sources such as turbulence from the wind tunnel freestream or the lifting surface wake.   

The geometry and dynamics of interacting rigid bodies and point vortices

We present some of our results on the geometry behind rigid bodies in perfect flows interacting with point vortices. We use symplectic reduction by stages to re-derive the equations of motion, and introduce a number of geometric structures along the way, most notably a special principal fiber bundle with connection, which encapsulates the response of the fluid to motions of the rigid body. As an aside, we show that a number of classical results, such as the expression for the Kutta-Joukowski force on a rigid body with circulation, or the form of the interaction between the vortices and the body, are consequences of the fact that the curvature of this connection is non-zero.   

LES of the vortex wake developing behind a wing, also with initial velocity deficit due to friction drag

LES of vortex wakes behind a wing with elliptical loading and at very high $Re$ are presented. The efficient combination of the Vortex-In-Cell and the Parallel Fast Multipole methods is used (Cocle et al., J. Comput. Phys., in press). A realistic near wake model is used, taking into account both the induced drag (vortex sheet) and the friction drag (momentum deficit due to boundary layers). Most methods can usually only afford time-developing (T-D) simulations (i.e., assuming periodicity in axial direction). To quantify the relevance, or not, of such simplification, space-developing (S-D) simulations were also performed, down to ten wingspans. For both cases, short wavelength instabilities rapidly develop in the wake center part, due to the momentum deficit, and the flow rapidly becomes turbulent. Surrounding the rolling-up vortices, helical instabilities also grow and deform them. Yet, the two formed far wake vortices remain tight (small core) and with a significant residual axial velocity deficit in the core region (order of the max azimuthal velocity). In the S-D case, the deficit is further enhanced, due to the complex spiral roll-up; moreover, the flow becomes turbulent faster.   

Analysis of an idealized body-vortex systems

We explore the class of dynamical systems consisting of a body, N point vortices, and one or more passive particles in an ideal, unbounded, planar fluid. The body is represented by a closed curve and is free to move in response to the fluid motion. 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 velocity of the body. The equations of motion for this kind of system are reasonably well in hand. They can be analyzed using techniques from the theory of dynamical systems with a finite number of degrees of freedom. The simplest such system, a single point vortex and a circular body, is integrable. If we add vortices, or change other features of the system such as the body shape, the motion may become chaotic. Various solutions are shown and analyzed with an emphasis on the transition to chaos and its physical meaning. The motion of passively advected fluid particles is also investigated. This class of systems provides a rich family of few-degree-of-freedom systems that capture essential fluid-body interaction physics.   

The effect of varying downstream cylinder angle on vortex shedding from tandem cylinders

Tandem cylinders in cross-flow are typically categorized into three flow regimes depending on the longitudinal pitch ratio, $L/D$. For $1 [Preview Abstract]