Bulletin of the American Physical Society
2006 59th Annual Meeting of the APS Division of Fluid Dynamics
Sunday–Tuesday, November 19–21, 2006; Tampa Bay, Florida
Session GI: Vortex Dynamics and 3D Vortex Flows IV |
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Chair: Fazle Hussain, University of Houston Room: Tampa Marriott Waterside Hotel and Marina Meeting Room 5 |
Monday, November 20, 2006 10:30AM - 10:43AM |
GI.00001: The effect of buoyancy on vortex breakdown in a swirling jet Jacob Cohen, Dina Mourtazin The purpose of this experimental study is to explore the effect of buoyancy on vortex breakdown (VB) in swirling jets. Three non-dimensional parameters govern the flow: the jet exit Reynolds number, the swirl ratio and the Richardson number (buoyancy). The experimental apparatus consists of a vertical swirling water jet which discharges into a large tank. Moderate values of the Reynolds number are used in the range of $150\leq Re \leq 600$. Swirl is imparted onto the jet in a rotating chamber whereas the temperature difference between the jet and its surrounding is established by passing the jet through a heat exchanger, immersed in a circulating water bath with a controlled temperature. Vector maps of the vertical mid-plane and horizontal cross-sections are obtained by PIV measurements. It is demonstrated that VB can be effectively suppressed (enhanced) by prescribing a negative (positive) temperature difference between the jet core and its surrounding fluid. Moreover, the experimental critical swirl ratio for the appearance of VB is found to be in good agreement with a simple criterion, originally derived by Billant, Chomaz and Huerre ({\em J. Fluid Mech.}, 1998, {\bf 376} p. 183), for isothermal swirling jets and extended here to include buoyancy effects. The transition of VB from a closed bubble to an open cone configuration is mapped in terms of the Reynolds and Richardson numbers. [Preview Abstract] |
Monday, November 20, 2006 10:43AM - 10:56AM |
GI.00002: Vortex merging in stably stratified fluid Laura Brandt, Keiko Nomura The merging of a pair of symmetric, horizontally oriented vortices in a fluid with and without stable stratification is investigated. Two-dimensional numerical simulations are performed for a range of flow conditions. Results show the three phases of vortex merger: the first diffusive/adjustment phase, the convective phase, and the second diffusive phase. In general, the evolution of the flow depends on the relative significance of viscous, convective, and stratification effects, as characterized by the Reynolds number and Froude number. Analysis of unstratified flow elucidates the key underlying mechanisms of convective vortex merger and the relative significance of filamentation and mutual core entrainment; the latter being dominant and initiated by the interaction of strain rate and vorticity gradient near the center of rotation. For flows with low Froude numbers (moderate to strong stratification), the convective phase is significantly reduced and merging occurs sooner. This is attributed to the secondary flow associated with baroclinic torque, which advects the primary vortices towards each other and enhances the strain rate-vorticity gradient interaction, resulting in earlier core entrainment. [Preview Abstract] |
Monday, November 20, 2006 10:56AM - 11:09AM |
GI.00003: Stability of a family of uniform vortices related to vortex configurations before merging P. Luzzatto-Fegiz, C. H. K. Williamson Motivated by the merger of two corotating vortices, Cerretelli {\&} Williamson (JFM 2003) discovered a family of uniform vorticity patches representing the continuation of two corotating vortices into a single ``dumbbell'' shape. This branch of solutions passes through a bifurcation from the Kirchhoff ellipses (discovered by Kamm 1987 and Saffman 1988) and ends into a cat's eye shape. By using a more accurate method for equilibrium shape calculation, we find some differences in the equilibrium shapes to those discovered by Cerretelli {\&} Williamson, particularly near the topological change (from a two-vortex to a single vortex shape). We implement the approach of Dritschel (1985), and show that all the simply connected shapes are unstable to a three-fold perturbation, while a regime of the two-vortex shapes nearing the topological change is unstable to a two-fold antisymmetric perturbation. The stability of two patches has been source of debate in the literature. Saffman {\&} Szeto (1980) predicted exchange of stability at an extremum in energy and angular momentum; on the other hand, Dritschel (1985) found that conditions for instability from linear analysis did not match those coming from the energy criterion. In the present work, we find precise agreement between results from linear analysis and energy criterion, in accordance with the more recent work of Kamm (1987) and Dritschel (1995). [Preview Abstract] |
Monday, November 20, 2006 11:09AM - 11:22AM |
GI.00004: Flow Instability and Flow Control Scaling Laws Daniel Van Ness, Thomas Corke, Scott Morris A flow instability that is receptive to perturbations is present in the tip clearance leakage flow over the tip of a turbine blade. This instability was investigated through the introduction of active flow control in the viscous flow field. Control was implemented in the form of a dielectric barrier discharge created by a weakly-ionized plasma actuation arrangement. The experimental setup consisted of a low-speed linear turbine cascade made up of an array of nine Pratt \& Whitney ``PakB'' turbine blades. This idealized cascade configuration was used to examine the tip clearance leakage flow that exists within the low pressure turbine stage of a gas-turbine engine. The center blade of the cascade array had a variable tip clearance up to five percent chord. Reynolds numbers based on axial blade chord varied from $10^4$ to $10^5$. Multi-port pressure probe measurements, as well as Stereo Particle Image Velocimetry were used to document the dependence of the instability on the frequency and amplitude of flow control perturbations. Scaling laws based on the variation of blade tip clearance height and inflow conditions were investigated. These results permitted an improved understanding of the mechanism of flow instability. [Preview Abstract] |
Monday, November 20, 2006 11:22AM - 11:35AM |
GI.00005: Modification of vortex ring formation using dilute polymer solution Daniel Jordan, Michael Krane, Joel Peltier, Eric Patterson, Arnold Fontaine This talk will present the results of an experimental study to determine the effect of dilute polymer solution on the formation of a vortex ring. Experiments were conducted in a large, glass tank, filled with water. Vortex rings were produced by injecting a slug of dilute polymer solution into the tank through a nozzle. The injection was controlled by a prescribed piston motion in the nozzle. For the same piston motion, vortex rings were produced for 3 concentrations of the polymer solution, including one with no polymer. The vortex ring flowfield was measured using DPIV. Differences between the 3 cases of polymer concentration in vortex ring formation time, circulation, size, and convection speed are presented. [Preview Abstract] |
Monday, November 20, 2006 11:35AM - 11:48AM |
GI.00006: Non Linear Base Flow Modification by Streamwise Vortices Induced by Vortex Generators Application to the Control of Separated Flows Thomas Duriez, Jean Luc Aider, Jose E. Wesfreid Vortex generators (VGs) are a common way to perform flow control thought their actual effect on a generic flow is mainly unknown. In order to find determinant physical parameters which can be used to optimize dimensions, position and actuation of vortex generators we have studied the effect of solid cylinder vortex generators on a flat plate boundary layer. Using two-component PIV measurement and 3D reconstruction we show the existence of a boundary layer modulation due to counter rotating streamwise vortices. By analyzing the 3D velocity field we extract the non linear part of this modulation (and especially the quadratic non linear zeroth mode) which is responsible for the mean flow modification. This parametric study gives the growth rate of non linear perturbations and the properties of the spanwise modulation depending on VGs spacing and Reynolds number. These are determinant physical parameters of the boundary layer modification by the VGs that can be used to their efficient design and control. We finally compare these results to the average modification of a separated flow over a smoothly contoured ramp by such cylinder vortex generators. [Preview Abstract] |
Monday, November 20, 2006 11:48AM - 12:01PM |
GI.00007: Nonlinear evolution of optimal transient growth modes in a vortex column Fazle Hussain, D.S. Pradeep The transient growth of optimal modes -- obtained through linear analysis -- is pursued via direct numerical simulation (DNS). Evolutions of both individual modes in isolation and random superpositions of several modes are studied. Increasing initial amplitude decreases both growth and growth period. Thus nonlinear effects set an ``optimal'' initial amplitude that maximizes energy growth. Radially outward transport of vortex filaments organized into dipoles removes radial vorticity -- essential to transient growth - from regions of large strain; this nonlinear mechanism thereby diminishes production. Even a single mode's evolution reproduces the phenomena seen in a vortex interacting with fully developed ambient turbulence: (a) growth of strong core perturbations in the form of bending waves; (b) appearance of finer-scale vortex filaments (threads) wrapping around the column; and (c) accelerated vortex decay (beyond the viscous rate). Core fluctuations are seen to amplify even as the external turbulence decays (with intensities exceeding 40{\%}); thus core breakdown (transition) appears likely in high-Re practical flows (e.g. the aircraft wake). The vortex dynamics of dipole formation and motion suggest a radial vorticity regeneration mechanism leading to sustained turbulence production at Re higher than attained by our DNS. [Preview Abstract] |
Monday, November 20, 2006 12:01PM - 12:14PM |
GI.00008: Stability of an inviscid point vortex pair near a boundary with sources and sinks Zachary Parvin, Paul Krueger The dynamical system representing the 2D movement of a point vortex pair in inviscid flow near a flat and curved body is investigated, with the proposed application of deflecting water particles in the atmosphere during flight to prevent icing. The specific boundary shapes considered are a flat surface perpendicular to the oncoming flow, a circle, and a circle with preceding fins aligned with the oncoming flow. The fixed points of the uncontrolled vortex system are found to be unstable, so steady sources and sinks are added on the boundary to stabilize the system. Certain strength and location combinations are screened for feasibility in the anticipated application and tested numerically in order to find and maximize the size of the stable region within the flow. [Preview Abstract] |
Monday, November 20, 2006 12:14PM - 12:27PM |
GI.00009: Vortex shedding and Maxwell's problem Sebastien Michelin, Stefan Llewellyn Smith The coupled problem of a flow around a solid body has applications from the fall of objects in a fluid to the computation of forces on wind-exposed structures. A simplified 2D model is proposed here for the interaction between solid bodies and potential flows. Potential flows over sharp edges generate singular velocities at the edges. To satisfy the Kutta condition, vorticity sheets must be shed from the edges to remove these singularities. Here 2D vorticity sheets are represented as discrete point-vortices with monotically varying intensity. From the fluid momentum conservation, an equation of motion for these vortices, the Brown and Michael equation, is derived and mechanical efforts applied by the fluid on the body are computed. The set of dynamical equations obtained for the fluid-body system is closed and is applied to Maxwell's problem of the 2D fall of a plate in an inviscid fluid initially at rest. [Preview Abstract] |
Monday, November 20, 2006 12:27PM - 12:40PM |
GI.00010: Analysis of vortical flow with axial swirl and toroidal circulation Sukalyan Bhattacharya Vortical flows with an axial swirl and a toroidal circulation can be observed in a wide range of fluid mechanical phenomena such as flow around rotary machines or natural vortices like tornadoes and hurricanes. These flows can be described by a general scalar equation if incompressible fluid and negligible viscous dissipation are assumed. We consider one of the simpler cases of this general formulation where the involved equation has a resemblance with the governing equation of the hydrogen problem. As a result, we obtain a quantization relation similar to the expression of quantized energies in an hydrogen atom. We solve the equation for two systems. First, we consider three- dimensional vortices confined between two parallel walls. Our examples include flows between two infinite plates, inside and outside of a vertical cylinder bounded at the ends by walls, and in an axially confined annular region. Then we also use our formulation to compute highly chaotic velocity fields with three-dimensional vortical structures which qualitatively mimic the features of physical flows. Hence, these solutions may be used in modeling of complicated flow systems. [Preview Abstract] |
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