Bulletin of the American Physical Society
67th Annual Meeting of the APS Division of Fluid Dynamics
Volume 59, Number 20
Sunday–Tuesday, November 23–25, 2014; San Francisco, California
Session A16: Free-Surface Flows I: Impacts |
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Chair: Jesse Belden, Naval Underwater System Center Room: 2000 |
Sunday, November 23, 2014 8:00AM - 8:13AM |
A16.00001: Oblique impact of water-skipping elastic spheres Jesse Belden, Tadd Truscott, Randy Hurd, Michael Jandron, Allan Bower Highly compliant elastic spheres possess remarkable water skipping capabilities. High-speed video reveals that, upon impact with the water, the balls create a cavity and deform significantly. The flattened spheres resemble skipping stones and this augmented geometry results in enhanced lift that causes the ball to launch back into the air. This deformation also excites elastic vibration modes within the sphere. A numerical model reveals that the vibrations are initiated by a stress concentration developed in the early moments of impact. In one mode, an elastic wave propagates around the sphere periphery and may impact the water surface, resulting in an energy loss from the sphere. Thus two timescales govern the success of skipping: the total collision time of impact must be less than the deformation time associated with material vibration. Using a simplified analytical model, we derive the expected scaling of each time in terms of a dimensionless ratio of material shear modulus to fluid inertia forces, $G / \rho U^2$. Experiments over a range of parameters validate this scaling and result in a regime diagram that distinguishes different types of skipping. We identify critical relations for the material properties and impact conditions to achieve skipping. [Preview Abstract] |
Sunday, November 23, 2014 8:13AM - 8:26AM |
A16.00002: Performance enhancing water skipping: successive free surface impacts of elastic spheres Randy Hurd, Tadd Truscott, Jesse Belden From naval gunners skipping cannonballs to children skipping stones, physicists have long been enamored with the repeated ricochet of objects on the water surface. Elastic spheres, such as the toy Waboba ball, make water skipping more accessible to the masses by expanding the range of impact parameters over which objects can be skipped. For example, it is not difficult to achieve more than twenty skips with such spheres, where skipping a stone twenty times is very difficult. In this talk we discuss the dynamics of water skipping elastic spheres over several successive skips. High-speed video captured using a unique experimental setup reveals how dynamics change with each skip as a result of lost kinetic energy. We place these observations in the context of previous work on single oblique impacts to identify material vibration modes that are excited during ricochet. The material modes excited with each successive impact are seen to decay from high-energy modes to low energy modes until water entry finally occurs. A model for estimating skipping outcome from initial conditions is proposed. [Preview Abstract] |
Sunday, November 23, 2014 8:26AM - 8:39AM |
A16.00003: Impact with dynamic surface tension Laurent Duchemin, Nicolas Vandenberghe We study impacts of a rigid body on a thin elastic sheet floating on a liquid. When struck by a solid object of small size, the elastic sheet deforms and waves propagate in and on the membrane. The impact triggers a longitudinal elastic wave effectively stretching the membrane. The hydro-elastic transverse wave that propagates in the stretched domain is similar to capillary waves on a free surface with an equivalent ``surface tension'' that results from the stretching of the elastic membrane. Two limiting cases, for which a self-similar solution can be computed, corresponding to short and long times are identified. Surprisingly, our study reveals that the fluid-body system behaves as a regular liquid-gas interface, but with an effective surface tension coefficient that scales linearly with the impact velocity. [Preview Abstract] |
Sunday, November 23, 2014 8:39AM - 8:52AM |
A16.00004: Resolution of the singularities in the water impact problem: compressibility and viscosity effects Rouslan Krechetnikov This work presents an analysis of the flow structure resulting from the flat plate impact on the surface of a compressible viscous liquid at zero deadrise angle. The key goals are to elucidate the effects of compressibility and viscosity and to resolve both near the plate edge, $r \rightarrow 0$, and the early times, $t \rightarrow 0$, limit singularities in the classical incompressible inviscid pressure-impulse theory. The constructed solution is contrasted to its incompressible flow counterpart, which allows one to identify the characteristic time and spatial scales of each distinct stage of the flow evolution, as defined by different governing physical mechanisms. [Preview Abstract] |
Sunday, November 23, 2014 8:52AM - 9:05AM |
A16.00005: Water Entry of Deformable Spheres Tate Fanning, Randy Hurd, Jesse Belden, Tadd Truscott We examine the water entry characteristics and cavity dynamics of highly deformable elastic spheres at high Reynolds numbers (10$^{5})$ using high-speed photography and image processing techniques. Upon impact normal to a free surface, these elastic spheres undergo significant deformation. We have observed principal stretches on the order of 1.6 diameters for the most compliant spheres. This initial deformation sets up an oscillatory vibration mode in the sphere that persists throughout its descent through the water column. These oscillations disturb normal cavity formation, resulting in the formation of a periodic, nodular cavity. A comprehensive experimental study allows for prediction of cavity shape, pinch off depth, and time to pinch off. Decreasing sphere stiffness results in decreased pinch off depths, and increased time to pinch off over the range of Reynolds numbers tested. [Preview Abstract] |
Sunday, November 23, 2014 9:05AM - 9:18AM |
A16.00006: Flipping over: inversion characteristics of a buoyant cylindrical puck during oblique water impact Zachary Smith, Tadd Truscott The Apollo Command Module had a tendency to flip over upon impact with the ocean surface after returning from space (9/19 times). In an effort to improve upon this idea for potential missions to Saturn's moon Titan, we present experimental results of a simplified buoyant cylindrical puck impacting the water surface. We examine the dependence of inversion upon vertical and horizontal velocity, center of gravity, and the pitch angle of the puck relative to the free surface. An analytical model is developed which characterizes inversion. High-speed images reveal that the puck does not completely submerge upon impact. Instead, the top of the puck remains above the water surface via a contact line attachment to the cavity. The asymmetric cavity then collapses, applying a moment, which can be sufficient to invert the puck after impact. [Preview Abstract] |
Sunday, November 23, 2014 9:18AM - 9:31AM |
A16.00007: Investigation of the Entrainment Phenomenon Using a Scaling Approach Aravind Kishore, Urmila Ghia Air entrainment is a commonly observed phenomenon; we see it when filling a glass with water from a faucet, in the frothing of the ocean surface, in white water rapids, etc. The focus of our work is the numerical simulation of the entrainment phenomenon associated with laminar plunging jets. With increasing jet velocity, the interfacial cusp formed between the jet and the liquid pool becomes sharper. At a critical jet velocity, entrainment inception occurs, i.e., the interfacial cusp breaks, the interface ruptures, and air is pulled into the liquid pool. We conduct two-fluid simulations using the Volume-Of-Fluid (VOF) methodology. The large range of length scales in the flow presents a major computational challenge. We postulate an approach based on scaling of the underlying physics and this helps alleviate the constraints that the physics poses on the numerical method. The approach is validated using a simple flow configuration - a cylinder rotating at an interface between two fluids. Our simulations capture the sharpening of the interfacial cusp, and the sudden rupture of the interface. The predicted critical entrainment velocities are within 1{\%} of experimental data, thereby providing confidence in the approach. [Preview Abstract] |
Sunday, November 23, 2014 9:31AM - 9:44AM |
A16.00008: The effects of surface tension on the initial development of a free surface adjacent to an accelerated plate Jamal Uddin, David Needham When a vertical rigid plate is uniformly accelerated from rest into an initially stationary layer of inviscid incompressible fluid, the free surface will undergo a deformation in the locality of the intersection point between the free surface and the plate. This deformation of the free surface will, in the early stages, cause a jet to rise up the plate. An understanding of the local structure of the free surface in the early stages of motion is vital in many situations and has been developed in detail by King {\&} Needham (1994). In this work we consider the effects of introducing weak surface tension, characterized by the inverse Weber number, W, into the problem considered by King {\&} Needham (1994). Our approach is based upon matched asymptotic expansions as W to 0. It is found that four asymptotic regions are needed to describe the problem. The three largest regions have analytical solutions whilst a numerical method based on finite differences is used to solve the time dependent harmonic boundary value problem in the last region. We also present some preliminary comparisons between experiments and theory. [Preview Abstract] |
Sunday, November 23, 2014 9:44AM - 9:57AM |
A16.00009: On the cusps bordering liquid sheets Jose Manuel Gordillo, Henri Lhuissier, Emmanuel Villermaux The rim at the edge of a steady radially expanding liquid sheet, or bordering a hole expanding in a liquid film, is naturally indented. It presents a collection of cusps at the tip of which the liquid concentrates and is ejected. An experimental description of these cusps for a stationary flat inviscid Savart sheet, formed by the normal impact of a jet with diameter $d$ and velocity $u$ against a solid disk, is given. We identify the stable node-jet structure responsible for the deflection of the incoming flow at the rim and demonstrate how the cusps are the structures that accommodate for both mass and momentum conservation at the sheet edge. Their shape, their number around the sheet, and the residual momentum carried by the ejected liquid are computed. Our model reproduces the experimental observations, correcting the classical interpretation of Savart's experiments first given by Taylor, who proposed that the radius of the sheet is given by $R=d\,We/16$, with a Weber $We$ number based on $d$ and $u$. Indeed, Taylor's picture disregards that the sheet is not circular, that the liquid is ejected with a non-vanishing remnant radial momentum at the sheet edge and, hence, that the actual radius of the sheet is smaller than $R$. [Preview Abstract] |
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