Bulletin of the American Physical Society
66th Annual Meeting of the APS Division of Fluid Dynamics
Volume 58, Number 18
Sunday–Tuesday, November 24–26, 2013; Pittsburgh, Pennsylvania
Session H32: Viscous Flows II: Flows in Viscous Fluids |
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Chair: David Saintillan, University of Illinois at Urbana-Champaign Room: 403 |
Monday, November 25, 2013 10:30AM - 10:43AM |
H32.00001: Motion of a Bellows and a Free Surface in a Closed Vibrated Liquid-Filled Container J.R. Torczynski, L.A. Romero, T.J. O'Hern The coupled motion of a bellows and an idealized free surface in a closed container that is filled with an incompressible viscous liquid and that is vibrated vertically is investigated computationally and theoretically. The bellows and the free surface exhibit rectified motion in the sense that their displacements from their equilibrium positions averaged over a cycle are nonzero. Two types of rectification that arise from two sources of nonlinearity are identified. ``Geometric rectification'' results from the time variation of the bellows/free-surface geometry. ``Advective rectification'' results from the advection term in the Navier-Stokes equations. An approximate theory based on these ideas agrees well with direct numerical simulations over a broad range of frequencies from well below to well above resonance. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000. [Preview Abstract] |
Monday, November 25, 2013 10:43AM - 10:56AM |
H32.00002: On the inertial motions of liquid-filled rigid bodies Giusy Mazzone, Giovanni Galdi, Paolo Zunino We consider a rigid body with a cavity completely filled by a viscous liquid and study the inertial motions of the system liquid-filled rigid body $\mathcal S$. The equations governing the motion of this coupled system are given by the Navier-Stokes equations and the equations of the balance of the total angular momentum of $\mathcal S$ in absence of external forces and torques. Given any initial motion to the coupled system, characterized by an initial relative velocity of the fluid and an initial total angular momentum, we give a complete description of the behavior that the system liquid-filled rigid body will show at large times. From both analytical and numerical viewpoints, we are able to prove a longstanding conjecture stated by Zhukovskii, namely that $\mathcal S$ will eventually reach a steady state which is a rigid body permanent rotation. In other words, the liquid goes to rest with respect to the rigid body and the coupled system will rotate as a whole rigid body, with a constant angular velocity that is directed along one of the principal axes of inertia of the system. [Preview Abstract] |
Monday, November 25, 2013 10:56AM - 11:09AM |
H32.00003: Trajectory and flow properties for a rod spinning in a viscous fluid: An asymptotic solution with a no-slip plane Longhua Zhao, Roberto Camassa, Terry Jo Leiterman, Richard McLaughlin, Leandra Vicci Utilizing singularity theory and the slender body theory, asymptotic solutions are constructed for a slender body sweeping out a double cone or single cone in free space in the low Reynolds number regime. The asymptotic solutions are compared quantitatively with the exact solutions for a prolate spheroid performing similar motion. With a set of singularities, Blakelet, an asymptotic solution is developed for a slender cylinder attached to a no-slip plane and sweeping out an upright cone. The no-slip boundary condition is satisfied exactly. Trajectory and flow properties are examined with special attention paid to the case study on slenderness between the exact and asymptotic free space solutions. For flow with no-slip plane, the theoretical prediction is compared with the experimental data, which shows good agreement. Far field asymptotic analysis is presented for the asymptotic velocity when the slender body precesses cones in free space and with no-slip plane. When the cone is tilted, the asymptotic solution is constructed in the lab frame, and the experimental data are reported compared with the theoretical prediction. This study is of direct use to nano-scale actuated fluidics where similar epicyclical behavior has been observed. [Preview Abstract] |
Monday, November 25, 2013 11:09AM - 11:22AM |
H32.00004: Three-dimensional Developing Flow in a Long Serpentine Channel Surya P. Vanka Serpentine wavy channels are often used as fin passages in compact heat exchangers because of their increased heat transfer performance. However, their benefit is seen only in the unsteady flow regime, and in the turbulent regime. In this work, we study the three-dimensional developing flow in a wavy passage using a finite volume fractional-step Navier-Stokes solver. The geometry consists of a straight approach section, several (8) waves and a stratight section at the end. A curvilinear grid is used to represent the flow domain. Both the steady and unsteady flow regimes are computed by systematically increasing the Reynolds numbers. The effects of the wave amplitude and the wave length are also studied. The structure of the developing flow is presented for different parameter selections. The spanwise structure of the flow on the curved surfaces, and the formation of the recirculating regions in the troughs are presented. Pressure drop characteristics in the developing region are compared with those in the fully-developed periodic region. [Preview Abstract] |
Monday, November 25, 2013 11:22AM - 11:35AM |
H32.00005: The sedimentation of flexible filaments: Shapes, trajectories, and clouds Saverio Spagnolie, Lei Li, Harishankar Manikantan, David Saintillan The dynamics of a flexible filament sedimenting in a viscous fluid (Stokes flow) are investigated. Compared to the well-studied case of sedimenting rigid rods, the introduction of filament compliance is shown to cause a significant alteration in the long-time sedimentation orientation and filament geometry. A model is developed by balancing viscous, elastic, and gravitational forces in a slender-body theory, and the filament dynamics are characterized by a dimensionless elasto-gravitation number. In the weakly flexible regime, a multiple-scale asymptotic expansion is used to obtain expressions for filament translations, rotations, and shapes, which match excellently with full numerical simulations. Furthermore, trajectories of sedimenting flexible filaments, unlike their rigid counterparts, are restricted to a cloud whose envelope is determined by the elasto-gravitation number. [Preview Abstract] |
Monday, November 25, 2013 11:35AM - 11:48AM |
H32.00006: The sedimentation of flexible filaments: A buckling instability Harishankar Manikantan, David Saintillan, Lei Li, Saverio Spagnolie An elastic filament sedimenting in a viscous fluid can lead to complex deformations and dynamics due to the non-trivial interplay between gravity, viscous stresses and its internal elastic forces. One such dramatic case is the buckling of a flexible filament placed with its long axis parallel to gravity. Using slender-body theory for low-Reynolds number flows, we first show that a non-uniform tension is induced in the filament due primarily to a non-uniform shape and secondarily to non-local hydrodynamic interations. This tension acts to compress the filament in its leading half and can lead to a buckling instability in the highly flexible regime, which we characterize via a dimensionless elasto-gravitation number. We derive a dispersion relation that clearly illustrates this competing effect between tension and elastic rigidity, and also suggests that the instability travels as waves in the direction opposite gravity. We then turn to numerical simulations to verify this, and see that waves grow and travel as predicted. We also look at linear eigenmodes of the governing equation, and the mode shapes so obtained agree well with those observed in simulations. [Preview Abstract] |
Monday, November 25, 2013 11:48AM - 12:01PM |
H32.00007: Quantitative Viscosity Field Measurement during Viscous Fingering by Imaging Fluorescence from a Viscosity-Sensitive Molecular Probe Bradley Dice, Michael Rawat, Simone Stewart, Patrick Bunton, Fabian Brau, Anne De Wit, John Pojman The two-dimensional spatio-temporal distribution of the viscosity field has been measured quantitatively during radial displacements of pure glycerol and a miscible solution of glycerol and water inside a horizontal Hele-Shaw cell. Ultraviolet-excited fluorescence from the viscosity-sensitive molecular probe Auramine O was imaged in situ during the displacement. Fluorescence intensity as a function of viscosity was calibrated using known values of viscosity for glycerol-water solutions from the literature. From this calibration, the two-dimensional spatio-temporal map of fluorescence allowed for reconstruction of the evolution of the viscosity field during either the stable displacement or the viscous fingering process. For the stable case the viscosity profile was compared to the known analytical solution. This technique should prove widely applicable for in situ viscosity measurements during flow instabilities subject to appropriate choice of molecular probe. [Preview Abstract] |
Monday, November 25, 2013 12:01PM - 12:14PM |
H32.00008: Low Reynolds number hydrodynamics of microstructured optical fiber fabrication Peter Buchak, Darren Crowdy, Yvonne Stokes Microstructured optical fibers (MOF's) derive novel optical capabilities from having large numbers of wavelength-scale channels. MOF's are fabricated by the capillary drawing of a molten glass preform at low Reynolds number, during which the cross section deforms under surface tension, with the result that the configuration of the channels in the fiber may differ from the perform. This unintended deformation is inadequately understood and is difficult to investigate experimentally. In this talk, we describe methods we have developed to model slender viscous fibers with multiply connected cross section, which make possible theoretical investigation of the deformation, with the aim of determining the preform configuration required to produce a fiber with a desired arrangement of channels. [Preview Abstract] |
Monday, November 25, 2013 12:14PM - 12:27PM |
H32.00009: Microstructured optical fibres: how do physical parameters influence the final geometry? Yvonne Stokes, Peter Buchak, Darren Crowdy Drawing of a microstructured optical fibre can be described by a 1D differential equation for the cross-sectional area as a function of axial position and a 2D classical Stokes-flow model for the evolution of the cross-sectional geometry as it moves along the fibre axis. These two models are coupled through the total length of the cross-sectional boundary. Physical parameters, including the initial preform geometry, the draw ratio and material properties, enter the model in non-trivial ways and affect the final fibre geometry. In this talk we will examine the coupled 1D and 2D models of fibre drawing to gain understanding of the influence of physical parameters on the final geometry, and also look at the existence and uniqueness of solutions. We aim to determine what fibre geometries can or cannot be obtained from a given initial preform. [Preview Abstract] |
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