Bulletin of the American Physical Society
64th Annual Meeting of the APS Division of Fluid Dynamics
Volume 56, Number 18
Sunday–Tuesday, November 20–22, 2011; Baltimore, Maryland
Session G15: Free-Surface Flows I |
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Chair: Alexandra Techet, Massachusetts Institute of Technology Room: 318 |
Monday, November 21, 2011 8:00AM - 8:13AM |
G15.00001: A regularised one-dimensional drop formation and coalescence model on a single Eulerian grid Theo Driessen, Roger Jeurissen, Herman Wijshoff, Arjan van der Bos, Jacco Snoeijer, Detlef Lohse Droplets with a well-controlled size and speed are required in many industrial and medical applications. In this work we study axisymmetric droplet formation from a piezo inkjet print head. The breakup of an axisymmetric viscous jet is considered in the lubrication approximation. The discretised equations are solved on a fixed equidistant one-dimensional Eulerian grid. The governing equations are implemented in a conservative second order accurate total variation diminishing (TVD) scheme, preventing the numerical diffusivity. Singularities that occur at pinchoff and coalescence are regularised by a small modification on the surface tension. The modification is of the order of the spatial step. This regularisation ensures that the solution of the presented numerical model converges to the exact solution of the breakup of a jet in the lubrication approximation. The results of the presented numerical model agree quantitatively with the analytical solution of the Rayleigh-Plateau instability, and with experimental results on the final stage of the Rayleigh-Plateau instability. [Preview Abstract] |
Monday, November 21, 2011 8:13AM - 8:26AM |
G15.00002: Splash and droplet ejection after disc impact on a liquid Ivo R. Peters, Devaraj van der Meer, Jose Manuel Gordillo When a circular disc hits a water surface, a thin sheet of liquid is ejected close to the edge of the disc. Surface tension deforms the tip of this sheet into a rim which, depending on the experimental conditions, becomes unstable and ejects small droplets. At the region very close to the edge of the disc and for times close to the moment of impact, we find that the liquid sheet shows a clear self-similar behavior for any value of the Weber number provided that $Fr=U^2/(gR_{disc})>1$. We demonstrate, by using both experimental results and boundary-integral simulations, that the ejection of droplets in this experiment is caused by a Rayleigh-Taylor instability. This results from a strong downwards pointing acceleration present in the liquid sheet, much larger than the gravitational acceleration. By determining the length-scale and the acceleration at the tip of the sheet, we show that the transition to droplet ejection occurs when the Bond number is of order 1. [Preview Abstract] |
Monday, November 21, 2011 8:26AM - 8:39AM |
G15.00003: Surface Seal in the Water-Entry of Hydrophobic Spheres Benjamin Jackson, Sunghwan Jung, Pavlos Vlachos We examine the surface seal phenomenon observed in the water entry of hydrophobic spheres. Using high speed shadowgraph imaging we experimentally investigate the dependence of surface seal time and critical pressure on projectile size, density, and impact velocity. In the initial stage of impact the projectile slams into the free surface projecting a splash curtain upward. As the projectile descends into the fluid, an air cavity forms behind it and eventually pinches off from the atmosphere. Previous studies have primarily focused on the low velocity case where surface seal does not occur and the events above the free surface are often ignored. As the projectile velocity increases, the pressure drop within the cavity increases. Surface seal occurs when this pressure drop exceeds a critical pressure and is characterized by the closure of the splash curtain. The splash curtain domes over and seals the cavity above the free surface. This dome closure emits a downward jet which propagates into the air cavity from above and affects the later cavity dynamics. We present scaling arguments for critical pressure and surface seal time based on our observations. [Preview Abstract] |
Monday, November 21, 2011 8:39AM - 8:52AM |
G15.00004: The Nearfield of a Shallow Angle Plunging Jet - Periodicity of Air Cavity Formation Suraj S. Deshpande, Mario F. Trujillo The plunging of a water jet into a quiescent water pool is investigated computationally, using the Volume-of-Fluid methodology in the framework of the open source utilities of OpenFOAM. For the shallow angle plunges ($\theta < \sim 20^{\circ}$), our computations and previous experiments at Dynaflow Inc. revealed a distinct periodicity in the formation of large air cavities in the nearfield. In this work, we analyze the periodicity and present a closed form expression to describe it. Our analysis, based on potential flow treatment, regards the cavity as a Rankine body [Oguz et al., JFM 1995] and its motion as that of a standing wave. For the jets considered ($Fr\sim O$(10), $Re\sim O(10^5)$, $We\sim O(10^3)$ and $\theta<\sim 20^{\circ}$.), the frequency of cavity formation was found to be related to the jet diameter and gravity, independent of viscous and surface tension effects. Our analysis, which is valid only for shallow plunges, is in excellent agreement with this observation. For steeper jets, we demonstrate that this periodicity vanishes and small air cavities are chaotically drawn into the pool. [Preview Abstract] |
Monday, November 21, 2011 8:52AM - 9:05AM |
G15.00005: Eggs in Milk: The Conclusion Ken Langley, Jeff Hendricks, Matthew Elverud, Dan Maynes, Tadd Truscott A hard-boiled egg spinning on a countertop and passing through a puddle of milk draws milk up the side of the egg and then ejects it at the maximum radius. This same phenomenon occurs for any partially submerged spinning object whose radius increases upward from the fluid surface (e.g., spheres, inverted cones, rings, etc.). In particular, spheres are used to investigate the behavior of this phenomenon and its sensitivity to experimental parameters. Three modes of ejection -- jets, sheets, and sheet break-up -- are identified, which are highly dependent on several parameters: viscosity, angular velocity, immersion depth of sphere, and sphere diameter. Experimental results are presented with comparisons to a theoretical model that is derived using integral conservation of momentum. This phenomenon can be used as a pump to easily remove fluids from shallow areas. [Preview Abstract] |
Monday, November 21, 2011 9:05AM - 9:18AM |
G15.00006: Angled wing air induction for microbubble drag reduction Yuichi Murai, Ichiro Kumagai, Yuji Tasaka, Yoshiaki Takahashi Interfacial dynamics above an angled wing which is submerged into shallow water is investigated. Our experimental study aims at designing a high-performance bubble generator for microbubble drag reduction in marine vehicles. The performance being parameterized by the size and the amount of bubbles is determined by flow physics which is represented by triple interference among the air layer, the water flow, and the solid wing. The wing gives rapid deformation of the interface as well as disturbance before downstream high-speed wave-breaking and further later bubble fragmentation with help of Kelvin-Helmholtz instability. We have already demonstrated several practical installation of the device onto commercial ships from small to large scale. The presentation deals with the visualization of the wing-above behavior of gas-liquid interface that triggers the generation of fine bubbles in its downstream layer. [Preview Abstract] |
Monday, November 21, 2011 9:18AM - 9:31AM |
G15.00007: DNS prediction of the properties of solitary waves running down a vertically falling film P.-K. Nguyen, V. Bontozoglou, S. Chakraborty, C. Ruyer-Quil The present work computes the properties of stationary, traveling wave by solving the Navier-Stokes equation using the Galerkin finite element method. Solitary-like waves are derived by considering a long enough computational domain and necessarily a strong mesh refinement in the vicinity of the solitary wave in order that the properties of the wave converge asymptotically to the true solitary limit. The solitary wave can be characterized by its maximum height, and phase speed in terms of the modified Reynolds number, $\delta=3^{4/3}Re^{11/9}Ka^{-1/3}$. Both the wave height and the phase speed curves exhibit inflection points in the transition region, then maxima at intermediate values of $\delta$, and finally a drop to a plateau at high enough $\delta$. These are unique characteristics of the full second-order model by Ruyer-Quil and Manneville. In particular, the behavior deep in high $\delta$ limit shows that (i) the phase speed tends asymptotically to a value almost unaffected by $Ka$, and (ii) the wave height increases roughly linearly with $Ka$, which underlines the stabilizing effect of viscous diffusion at low Kapitsa numbers. [Preview Abstract] |
Monday, November 21, 2011 9:31AM - 9:44AM |
G15.00008: Propagation of axisymmetric capillary waves along a periodically-pinned liquid cylinder: Bloch waves and scattering Likun Zhang, David Thiessen An open capillary channel consisting of a water-filled helical wire is useful for phase separation because of its ability to capture impacting droplets. Capillary wave packets are generated by the impact and transport energy from the impact zone. In order to understand the propagation characteristics, we develop a theoretical model for a simplified axisymmetric channel consisting of a liquid cylinder with the free surface pinned by a periodic array of rings. The theory is based on the Bloch theorem and an eigenfunction expansion. From the semi-analytical solution we have computed the band structure, dispersion relation, phase speed, group speed, and energy flux, as well as their dependence on channel parameters. Results are interpreted in terms of the single-ring scattering properties and compared to multiple scattering for finite ring arrays. [Preview Abstract] |
Monday, November 21, 2011 9:44AM - 9:57AM |
G15.00009: Scattering of axisymmetric capillary waves on a liquid cylinder by a pair of surface-pinning rings and the relation to liquid-bridge resonance David Thiessen, Likun Zhang We consider the scattering of time-harmonic axisymmetric capillary waves on an infinite inviscid liquid cylinder by two infinitesimal coaxial surface-pinning rings. A semi-analytical solution is obtained by solving the truncated system of equations based on an evanescent wave expansion. The computations find that there is an infinite set of discrete frequencies at which the transmission is total, and these frequencies are shown to correspond to the resonant frequencies of the liquid bridge that spans the rings. These frequencies are close to the resonant modes of an inviscid liquid bridge between two impenetrable disks. An approximate solution is also obtained for the case of widely spaced rings using single-ring scattering properties. The extension of the approximate method to the computation of capillary mode resonances for other geometries will be discussed. [Preview Abstract] |
Monday, November 21, 2011 9:57AM - 10:10AM |
G15.00010: Field-enhanced electrokinetic charge separation induced by thermocapillarity-driven flow in a liquid film Mathias Dietzel, Steffen Hardt Thermocapillary stresses acting tangentially to the interface of a thin liquid film in a wide slot subjected to a lateral thermal gradient induce a rotational flow pattern. We demonstrate analytically and numerically for an electrolyte as working fluid that this flow can be used to separate charges and induce a streaming potential based on the electrokinetic effect, converting thermal to electric energy. The charge separation efficiency is commonly spoiled by the circumstance that the excess ions accumulate in direct vicinity of the wall where frictional losses are highest. As an alternative, we impose a traverse electric field across the film so that excess ions also accumulate at the gas-liquid interface where the highest flow velocities occur. No power is needed to maintain the external field if the deformation of the interface remains negligibly small, requiring in turn sufficiently small applied thermal and electric gradients below critical values of hydrodynamic and electrostatic instabilities. We estimate the increase and the upper limit of the streaming potential as well as of the overall conversion efficiency as a function of the applied voltage and the film thickness scaled to the Debye length. [Preview Abstract] |
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