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 EK: Free Surface Flows II |
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Chair: William R.C. Phillips, University of Illinois at Urbana-Champaign Room: Tampa Marriott Waterside Hotel and Marina Meeting Room 4 |
Sunday, November 19, 2006 4:15PM - 4:28PM |
EK.00001: Instability of a negatively-buoyant fountain Peter Friedman, Vidya Vadakoot, William Meyer Experimental simulations were carried out to investigate the stability of negatively buoyant fountains by injecting glycerin-water mixtures into silicon oil and imaging the flow structure using PIV. The transition from a stable to an unstable fountain structure is strongly controlled by the Richardson number of the jet, and to a lesser extent, Reynolds number, viscosity ratio, Weber number and Vent geometry. Transition occurs at a nominal Ri = 1.0. In a cylindrical vent geometry, the only effect of the Reynolds number is in determining whether or not the fountain is laminar or turbulent, which can be fully accounted for by basing the Richardson number on the Root mean Square of the mean velocity. Viscosity ratio deviating from unity has the effect of stabilizing the flow structure and thereby reducing the Richardson number for transition to an unstable flow structure. Similarly, interfacial tension stabilizes the flow pattern resulting in a trend of increasing transition Richardson number with increasing Weber number. The results are valid in rectangular vents if the Richardson number and Reynolds number are based on the hydraulic diameter. [Preview Abstract] |
Sunday, November 19, 2006 4:28PM - 4:41PM |
EK.00002: Observation of transition behavior on oscillatory Marangoni flow of Low-Pr number liquid column Hiroei Sasaki, Satoshi Matsumoto, Takeshi Mashiko, Hiroaki Ohira, Shinichi Yoda, Erika Yoda, Nobuyuki Imaishi, Tetsuichi Motegi An experimental study on thermocapillary convection of low Prandtl number fluid was carried out to understand transition behavior to oscillatory flow. In this experiment, we use molten tin as the working fluid, which Prandtl number is \textit{Pr}$\sim $0.01. The liquid column of molten tin was formed between hot and cold disks in high vacuum chamber and the half-zone configuration was employed. We imposed temperature difference between top and bottom of liquid column to induce a marangoni convection. Temperature distribution at interface between liquid column and cold disk was measured by using several fine thermocouples. As a result, several oscillatory flow patterns were observed. In addition, we compared these results with numerical simulation and estimated the mode stractuers. [Preview Abstract] |
Sunday, November 19, 2006 4:41PM - 4:54PM |
EK.00003: Bouncing of a Jet off a Newtonian Liquid Surface Matthew Thrasher, Sunghwan Jung, Harry L. Swinney A viscous liquid stream plunging toward a horizontally moving bath of the same liquid can bounce off the surface without mixing with the bath's fluid. A thin layer of air separates the jet and the bath. The non-coalescing jet ramps off an indentation that it makes in the bath's surface. The jet then moves in a roughly parabolic flight until it hits the translating surface again, where it may bounce a second time. Similar rebounding phenomena, such as the Kaye effect, have been observed in non-Newtonian fluids. However, we report the first observations of a bouncing \emph{Newtonian} liquid jet. We observe the bouncing jet for many different liquids, including silicone oil. The bouncing jet is stable for a large range of parameters, including the oil's viscosity (50 to 520 mPa s), the jet's radius (0.05 to 0.12 cm), the jet's velocity at impact (40 to 170 cm/s, corresponding to nozzle heights 1.7 to 14 cm), and the bath's horizontal velocity (1 to 35 cm/s). The bouncing jet involves an interplay of viscous, inertial, surface, and gravitational forces. By initiating the jet in different ways, up to four stable configurations have been observed for the same experimental conditions. A video entry into the Gallery of Fluid Motion features this research. [Preview Abstract] |
Sunday, November 19, 2006 4:54PM - 5:07PM |
EK.00004: Onset of `stitching' in the fluid mechanical `sewing machine' Neil Ribe, John Lister, Sunny Chiu-Webster A thin thread of viscous fluid that falls on a moving belt acts like a fluid mechanical `sewing machine', exhibiting a rich variety of `stitch' patterns including meanders, side kicks, slanted loops, braiding, figures-of-eight, W-patterns, and period-doubled patterns (Chiu-Webster and Lister, J. Fluid Mech., in press). Using a numerical linear stability analysis based on asymptotic `slender thread' theory, we determine the critical belt speed and frequency of the first bifurcation, at which a steady dragged viscous thread becomes unstable to sideways oscillations (`meanders'). The predictions of the stability analysis agree closely with experimental measurements. Moreover, we find that the critical belt speed and frequency for meandering are nearly identical to the contact point migration speed and the frequency, respectively, of steady coiling of a viscous thread on a stationary surface, implying a remarkable degree of dynamical similarity between the two phenomena. [Preview Abstract] |
Sunday, November 19, 2006 5:07PM - 5:20PM |
EK.00005: Thread amplitudes and frequencies in a fluid mechanical `sewing machine' Stephen W. Morris, J.H.P. Dawes, John Lister, Stuart Dalziel A viscous thread falling on a surface exhibits the famous rope- coiling effect, in which the thread buckles to form loops. If the surface is replaced by a belt moving at speed $U$, the rotational symmetry of the buckling instability is broken and a wealth of interesting states are observed~(1). We experimentally studied this fluid mechanical `sewing machine' in a new, more precise apparatus. As $U$ is reduced, the stretched thread bifurcates into a meandering state in which the thread displacements are only transverse to the motion of the belt. We measured the amplitudes $A$ and frequency $\omega$ of the meandering close to the bifurcation. For small $U$, single- frequency meandering bifurcates to a two-frequency `figure 8' state, which contains a significant $2\omega$ component and parallel as well as transverse displacements. This eventually reverts to single-frequency coiling at smaller $U$. More complex, highly hysteretic states with additional harmonics are observed for larger nozzle heights. We propose to understand this zoology in terms of the generic amplitude equations appropriate for resonant interactions between three oscillatory modes with frequencies $\omega$, $2\omega$ and $3\omega$. The form of the amplitude equations captures both the axisymmetry of the $U=0$ coiling state and the symmetry-breaking effects induced by the moving belt.\\ (1) Chiu-Webster and Lister, J. Fluid Mech., in press. [Preview Abstract] |
Sunday, November 19, 2006 5:20PM - 5:33PM |
EK.00006: On Breakup Regime Transitions of Liquid Jets in Crossflow Khaled Sallam, Chee-Loon Ng, Ramprakash Sankarakrishnan An experimental and computational research is performed to study the breakup regime transitions of round liquid jets in uniform gaseous crossflow at normal temperature and pressure, large liquid/gas density ratios and small Ohnesorge numbers. Pulsed photography, shadowgraphy, and high-speed imaging were used to observe jet primary breakup regimes. The computational study analyzed the internal and external flow fields within the column, bag, and shear breakup regimes. Present results show that the column waves along the liquid jet are attributed to Rayleigh-Taylor instabilities. In bag breakup, the lower pressure along the sides of the jet pulled the liquid away from both the upwind and downwind surfaces of the liquid cross-section. In shear breakup, the flattened upwind surface pushed the liquid towards the two sides of the jet. The breakup of turbulent liquid jets was influenced by a new dimensionless number in terms of liquid/gas momentum ratio and the jet Weber number. [Preview Abstract] |
Sunday, November 19, 2006 5:33PM - 5:46PM |
EK.00007: Impulsively generated axisymmetric free surface waves and drops Kuan-Khoon Tjan, William R.C. Phillips The axisymmetric evolution of a body of liquid occupying the half-space subjected to a Gaussian impulse in pressure is considered. Under the inviscid assumption, the problem is recast into a Fredholm integral equation of the second kind. The non-dimensional parameters controlling the non-linear (due to the presence of a free surface and the Bernoulli equation) evolution are the Weber and the Froude numbers. Two different drop formation mechanisms are identified: one in which a nearly spherical drop is ejected away from the free surface when the Weber number is moderate and the Froude number is large. The second, as the Froude number is reduced, is a tear shape drop which is formed as the surface collapses onto itself under the influence of gravity. A phase diagram identifying the various regimes will be presented, depicting the above mentioned cases and also that when no drops are formed and the surface evolves into an axisymmetric wave. [Preview Abstract] |
Sunday, November 19, 2006 5:46PM - 5:59PM |
EK.00008: Jet formation from impulsive cavity collapse Arnaud Antkowiak, Nicolas Bremond, St\'ephane Le Diz\`es, Emmanuel Villermaux A cavity at a free liquid/gas interface collapsing due to an impulsive body force forms an intense concentrated jet. This is the paradigm for bubbles bursting at a liquid surface, the collapse of cavitation bubbles near a rigid boundary, collapsing voids following an impact, shaped charges, gravity waves colliding a dam, high amplitude Faraday waves, to quote a few examples among many. We address this problem by considering the axial impact of a cylindrical tube falling by gravity and filled with a liquid wetting the tube wall. Following the impact on a rigid floor, the curvature of the spherical meniscus initially fixed by the tube radius reverses violently, prelude of the birth of a rapid ascending jet. We derive the initial velocity and pressure field around the cavity just after the impact from Euler equations. They are insensitive to liquid viscosity and surface tension, consistently with detailed PIV measurements from high speed movies of the phenomenon. The extension to a cavity no more confined by rigid walls, the dynamics of the resulting jet and its final fragmentation will be considered as well. [Preview Abstract] |
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