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 FK: Rotating Flows |
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Chair: Hantao Ji, Princeton University Room: Tampa Marriott Waterside Hotel and Marina Meeting Room 4 |
Monday, November 20, 2006 8:00AM - 8:13AM |
FK.00001: Angular Momentum Transport in Rotating Shear Flow: Turbulence Michael J. Burin, Ethan Schartman, Hantao Ji We report on experiments investigating rotating shear flow at high Reynolds numbers (10$^{3}$ -- 10$^{6})$ within a wide-gap annular apparatus. For centrifugally-unstable flow regimes, the angular momentum distribution within the fluid interior is observed to be constant over radius, i.e. reset to marginal stability. Momentum transport due to turbulent fluctuations was ascertained locally using a two component synchronized LDV. The observed scaling of the transport with respect to Reynolds number is found to be consistent with datasets of torque in similar flows. We also have investigated cases where the turbulent transport is partially quenched by co-rotating the outer portion of the flow. This stabilization primarily entails a reduction of turbulent intensity; the effect upon the cross-correlation coefficient is insignificant. The similarity of these results to the suppression of turbulence in other systems, such as in rotating pipe flow, is briefly noted. [Preview Abstract] |
Monday, November 20, 2006 8:13AM - 8:26AM |
FK.00002: Angular Momentum Transport in Rotating Shear Flow: Quiescence Ethan Schartman, Michael J. Burin, Hantao Ji, Jeremy Goodman Phenomenological arguments have been made that sub-critical
turbulent transition can drive enhanced angular momentum
transport in linearly stable rotating shear flows. We present
the results of a search for such a sub-critical transition in a
small aspect ratio, wide-gap rotating shear flow. Fine control
of secondary flows induced by the axial boundaries is obtained
using two pairs of differentially rotatable end rings. The $ |
Monday, November 20, 2006 8:26AM - 8:39AM |
FK.00003: Mid-plane symmetry breaking in finite (axisymmetric) counter-rotating disk flow. Richard Hewitt, Andrew Hazel We consider the steady flow of an incompressible fluid driven by the counter rotation of two co-axial disks of {\em finite} radius. It is known that a von K\'arm\'an similarity solution is available in an infinite geometry and that this solution possesses a pitchfork bifurcation that breaks the mid-plane symmetry. In this work we seek similar bifurcations in the finite-domain flow and compare the resulting bifurcation structure with the similarity solution for increasing aspect ratios. We thus assess the applicability of the nonlinear similarity solutions to finite domains and explore the sensitivity of this structure to edge conditions that are implicitly neglected when assuming a self-similar flow. We show that the nonlinear structure of the finite-domain flow (even for large aspect ratios) may be rather different both quantitatively and qualitatively from the self-similar flow for general edge conditions. [Preview Abstract] |
Monday, November 20, 2006 8:39AM - 8:52AM |
FK.00004: Thermocapillary instabilities with crystal and feed rod rotation in laterally heated liquid bridge Laurent Martin Witkowski, Lyes Kahouadji, John S. Walker Rotation is involved in many industrial processes for crystal growth. The main reason is that heating is usually not uniform in the azimuthal direction. A drawback (or advantage) of rotation is that it modifies the flow originating from thermal or electromagnetic sources. In the needle-eye float-zone process, the optimum angular velocity of the feed rod and crystal is found empirically. The ratio of these velocities is often negative but not always. Early numerical studies focused on the baseflow of the melt and were restricted to axisymmetry. The main finding is that when rotation is large enough the flow is confined toward the periphery as a result of Taylor column effect. More recent research is devoted to the stability of thermocapillary convection to tridimensional disturbances either by direct numerical simulations or by linear analysis but few relate to the effect of rotation. In order to have a better understanding of the effect of rotation rate on the critical Marangoni number for a laterally heated liquid bridge, we have studied the stability of tridimensional perturbation by a linear analysis for various angular velocity ratio. The competition between different azimuthal modes has been explored and some interpretations are given. [Preview Abstract] |
Monday, November 20, 2006 8:52AM - 9:05AM |
FK.00005: Modeling of swirling axisymmetric heated jets Aline Cotel, Chinar Aphale, William Schultz The competing effects of buoyancy and swirl are investigated numerically in an axisymmetric jet. One question of interest is the amount of swirl necessary to keep a heated jet cohesive in large-scale environments. An integral model is used to predict axial dependence using similarity in r for velocity and temperature profiles. Hence, this model is also applicable to large-scale atmospheric flows such as tornadoes. The effect of swirl on the jet width and entrainment is studied closely. The inclusion of swirl and temperature of the jet fluid with integral matching over r results in a governing system consisting of three ODEs for momentum, continuity and energy. Density variations due to the heated jet are considered in only two terms, the body force (buoyancy) term in the axial momentum equation and the body force (centrifugal) term in the radial momentum equation. The effect of swirl on entrainment is enhanced only if the jet is heated, then the density gradients constrict the core. The assumed pressure decay with height (z) is justified on the basis of error introduced by the integral matching. The model can predict cases of high swirl that Fluent is unable to compute satisfactorily. [Preview Abstract] |
Monday, November 20, 2006 9:05AM - 9:18AM |
FK.00006: Comparison of FDM \& FEM Simulations of Rotating-lid Driven Cylindrical Flows. Michael Brazell, Erik Durkish, Brian Helenbrook, Daniel T. Valentine Steady-state solutions of lid-driven rotating flows in cylindrical containers were computed to compare results from the ETUDE-in-R finite difference method (FDM) and an {\it hp} finite element method. The FDM method was used to solve for the azimuthal components of vorticity and velocity, and the meridional stream function. The {\it hp} method was used to solve for the pressure and velocity. The computed flow fields are axisymmetric approximations of the Navier- Stokes equations. The test case is a container with aspect ratio of 2.5 and a Reynolds number of 2200. Comparison of the results of the two methods is consistent. The centerline velocity profile and the shape of the two-breakdown-bubble flow visualization compare favorably with the numerical predictions. Results are also reported for a three-breakdown-bubble experiment for aspect ratio of 3.3 and Reynolds number of 2780. The Lamb vector and the helicity density are examined to provide further insight into these flows. [Preview Abstract] |
Monday, November 20, 2006 9:18AM - 9:31AM |
FK.00007: Numerical simulation of the interaction of an unconfined vortex with a solid surface Luis Parras, Ramon Fernandez-Feria The interaction of an open vortex with a solid plane perpendicular to the axis of the vortex is analyzed numerically. We solve the axisymmetric, incompressible Navier-Stokes equations with boundary conditions that far away from the axis correspond to Long's near-inviscid similarity solution for an open vortex. Continuation techniques are used to solve the equations of motion for increasing Reynolds numbers. When this parameter is large enough, vortex breakdown occurs, producing a small region of reversed flow at the axis close to the solid plane. This region increases in size with the Reynolds number and, eventually, two breakdown bubbles appears at the axis. We also find non-uniqueness of the solutions at several ranges of the Reynolds number. At the end, for large Reynolds numbers, the region of reversed flow at the axis extends all along it, from near the plane to the flow exit far above the plane, where the flow tends to `Type II' Long's self-similar solution. Thus we show that of the two different similarity solutions found by Long for a given flow force, only that with negative axial velocity at the axis (Type II solution) is compatible with the viscous interaction of the vortex with a solid surface. This flow configuration is in agreement with observations of intense tornado-like vortices, where the flow at the axis is directed downwards, while the mean flow is directed upwards. *Supported by the Ministerio de Educacion y Ciencia of Spain (FIS04-00538). [Preview Abstract] |
Monday, November 20, 2006 9:31AM - 9:44AM |
FK.00008: An experimental investigation of air entrainment through viscous liquids in a horizontally rotating cylinder Antonino Carnevali Flow patterns produced inside a cylinder partly filled with a viscous liquid and rotated about its horizontal axis of symmetry have been discussed by many authors. We report here on a similar experiment where we have observed \textit{new} flow patterns at filling fractions $\ge $ 50{\%}. We will focus on the production of thin films of air triangular in shape but otherwise similar to those produced in a very different geometry by a viscous jet plunging into a bath, as elucidated by J. Eggers [Phys. Rev. Lett. \textbf{86}, 19] and E. Lorenceau and D. Quere' [Phys. Rev. Lett. \textbf{93}, 254501]. Two-dimensional drops of the viscous liquid move inside the thin film as a stable associated feature. As the angular velocity is lowered, the triangular area of the film becomes smaller and smaller until it squeezes the remaining drop into a cusp. Further decrease of the angular velocity causes the film to burst and squeeze the drop out into the surrounding liquid. One final observation unreported elsewhere is the formation of an inverted tear-drop bubble that remains stationary in the apparatus while the liquid rotates at significant speeds. [Preview Abstract] |
Monday, November 20, 2006 9:44AM - 9:57AM |
FK.00009: Stirring inertial particles in three-dimensional flows in a cylindrical container with exactly counter-rotating lids. Cristian Escauriaza, Fotis Sotiropoulos Transport and mixing characteristics for the steady flow in a container with exactly counter-rotating lids have been recently studied [Lackey and Sotiropoulos, Phys. Fluids 18, 053601 (2006)] demonstrating the chaotic Lagrangian dynamics, and stirring rates for 300\underline {$<$}Re\underline {$<$}850. The complex mixing characteristics of these flows can have a distinctive effect on the transport and stirring of inertial particles, which so far has not been fully explored in experimentally realizable flows. In this study, we carry out one-way coupling simulations to investigate in detail the inertial and gravity effects on spherical particles in these three-dimensional flows at different Reynolds numbers. Special emphasis will be given to the trapping of particles in invariant sets, and the interaction of inertial particles with the shear layer that produces the chaotic region. The effects of the Stokes and Froude numbers on stirring rates will be compared quantitatively with the previous results obtained for passive particles. [Preview Abstract] |
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