Effect of Surface Condition of a Sphere on Its Water-Entry Cavity

May, Albert

doi:10.1063/1.1699831

Cited by 131 publications

(39 citation statements)

References 3 publications

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“…The advent of high-speed cine-photography allowed for quantitative measurements, the first series of which explored the influence of the atmospheric pressure on the water entry of missiles (Gilbarg & Anderson 1948;Richardson 1948). Additional investigations of the water-entry cavity and surrounding flow field were performed by Birkhoff & Caywood (1949), Birkhoff & Isaacs (1951), Birkhoff & Zarantonello (1957) and Abelson (1970), but the most extensive ones were conducted by May (1951May ( , 1952May ( , 1975 with a view to naval ordinance applications.…”

Section: Introductionmentioning

confidence: 99%

Water entry of small hydrophobic spheres

2009

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We present the results of a combined experimental and theoretical investigation of the normal impact of hydrophobic spheres on a water surface. Particular attention is given to characterizing the shape of the resulting air cavity in the low Bond number limit, where cavity collapse is driven principally by surface tension rather than gravity. A parameter study reveals the dependence of the cavity structure on the governing dimensionless groups. A theoretical description based on the solution to the Rayleigh-Besant problem is developed to describe the evolution of the cavity shape and yields an analytical solution for the pinch-off time in the zero Bond number limit. The sphere's depth at cavity pinch-off is also computed in the low Weber number, quasi-static limit. Theoretical predictions compare favourably with our experimental observations in the low Bond number regime, and also yield new insight into the high Bond number regime considered by previous investigators. Discrepancies are rationalized in terms of the assumed form of the velocity field and neglect of the longitudinal component of curvature, which together preclude an accurate description of the cavity for depths less than the capillary length. Finally, we present a theoretical model for the evolution of the splash curtain formed at high Weber number and couple it with the underlying cavity dynamics.

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Section: Introductionmentioning

confidence: 99%

Water entry of small hydrophobic spheres

2009

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“…When the object is not locally flat, a splash will only be formed provided that certain conditions are fulfilled. These conditions can sometimes be as subtle as the wetting properties of a smooth sphere, as was shown by May (1951); Duez et al (2007).…”

Section: Introductionmentioning

confidence: 99%

Splash wave and crown breakup after disc impact on a liquid surface

2013

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In this paper we analyze the impact of a circular disc on a free surface using experiments, potential flow numerical simulations and theory. We focus our attention both on the study of the generation and possible breakup of the splash wave created after the impact and on the calculation of the force on the disc. We have experimentally found that drops are only ejected from the rim located at the top part of the splash -giving rise to what is known as the crown splash-if the impact Weber number exceeds a threshold value We crit ≃ 140. We explain this threshold by defining a local Bond number Bo tip based on the rim deceleration and its radius of curvature, with which we show using both numerical simulations and experiments that a crown splash only occurs when Bo tip 1, revealing that the rim disrupts due to a Rayleigh-Taylor instability. Neglecting the effect of air, we show that the flow in the region close to the disc edge possesses a Weber-numberdependent self-similar structure for every Weber number. From this we demonstrate that Bo tip ∝ We, explaining both why the transition to crown splash can be characterized in terms of the impact Weber number and why this transition occurs for W e crit ≃ 140.Next, including the effect of air, we have developed a theory which predicts the timevarying thickness of the very thin air cushion that is entrapped between the impacting solid and the liquid. Our analysis reveals that gas critically affect the velocity of propagation of the splash wave as well as the time-varying force on the disc, F D . The existence of the air layer also limits the range of times in which the self-similar solution is valid and, accordingly, the maximum deceleration experienced by the liquid rim, what sets the length scale of the splash drops ejected when W e > We crit .

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“…Today, digital high-speed cameras are widely used for imaging water-entry hydrodynamics. Extensive experimental investigations of water entry by spheres and projectiles are presented in Bell (1924), May & Woodhull (1948, 1950, Richardson (1948), May (1951), May & Hoover (1963) and Abelson (1970). …”

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confidence: 99%

Water entry of spinning spheres

2009

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The complex hydrodynamics of water entry by a spinning sphere are investigated experimentally for low Froude numbers. Standard billiard balls are shot down at the free surface with controlled spin around one horizontal axis. High-speed digital video sequences reveal unique hydrodynamic phenomena which vary with spin rate and impact velocity. As anticipated, the spinning motion induces a lift force on the sphere and thus causes significant curvature in the trajectory of the object along its descent, similar to a curveball pitch in baseball. However, the splash and cavity dynamics are highly altered for the spinning case compared to impact of a sphere without spin. As spin rate increases, the splash curtain and cavity form and collapse asymmetrically with a persistent wedge of fluid emerging across the centre of the cavity. The wedge is formed as the sphere drags fluid along the surface, due to the no-slip condition; the wedge crosses the cavity in the same time it takes the sphere to rotate one-half a revolution. The spin rate relaxation time plateaus to a constant for tangential velocities above half the translational velocity of the sphere. Non-dimensional time to pinch off scales with Froude number as does the depth of pinch-off; however, a clear mass ratio dependence is noted in the depth to pinch off data. A force model is used to evaluate the lift and drag forces on the sphere after impact; resulting forces follow similar trends to those found for spinning spheres in oncoming flow, but are altered as a result of the subsurface air cavity. Images of the cavity and splash evolution, as well as force data, are presented for a range of spin rates and impact speeds; the influence of sphere density and diameter are also considered. IntroductionThe water-entry problem, by itself, is directly relevant to many different applications: from ballistics (May 1975) and ship slamming (Faltinsen & Zhao 1997) to skipping stones (Rosellini et al. 2005) and Basilisk lizards (Glasheen & McMahon 1996). One of the geometrically most simple objects that can be studied is the sphere. This canonical shape impacting on the free surface does not, however, yield simple hydrodynamic results, and the results are even more complex when spin is introduced (Truscott & Techet 2006). An experimental study of the impact of a sphere, spinning transverse to its velocity, on a water surface is presented herein, offering a first look into how spin can affect water-entry behaviour. Figure 1 shows a comparison of the non-spinning (a) and spinning (b) impact of a standard billiard ball on the free surface. The air cavity and splash formed by the spinning sphere vary distinctly from the axisymmetric cavity formed with no spin. The subsurface air cavity bends along the trajectory of the spinning sphere, and the splash † Email address for correspondence: ahtechet@MIT.EDU curtain grows vertically and collapses asymmetrically. For the spinning water-entry problem, valuable insight into the physics can be drawn from both water entry and spinning sphere re...

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Effect of Surface Condition of a Sphere on Its Water-Entry Cavity

Cited by 131 publications

References 3 publications

Water entry of small hydrophobic spheres

Water entry of small hydrophobic spheres

Splash wave and crown breakup after disc impact on a liquid surface

Water entry of spinning spheres

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