The Virtual Mass of a Sphere Entering Water Vertically

May, Albert; Woodhull, Jean C.

doi:10.1063/1.1699592

Cited by 53 publications

(14 citation statements)

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“…Worthington & Cole (1897, 1900 and Worthington (1908) were the first to investigate cavity formation and splash characteristics produced by spheres impacting onto liquid surfaces using single-spark illumination photography. Following their work, Mallock (1918), Bell (1924) and Ramsauer & Dobke (1927) provided further descriptions of the observed cavity characteristics, while the first sets of quantitative results were presented by Gilbarg & Anderson (1948), Richardson (1948), May & Woodhull (1948, 1950 and May (1951May ( , 1952 who collectively investigated sphere impacts with water surfaces, highlighting the influence of atmospheric pressure, overall impact forces involved and the effect of the sphere wettability on the observed cavity and splash characteristics.…”

Section: Introductionmentioning

confidence: 99%

Water entry without surface seal: extended cavity formation

et al. 2014

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We report results from an experimental study of cavity formation during the impact of superhydrophobic spheres onto water. Using a simple splash-guard mechanism, we block the spray emerging during initial contact from closing thus eliminating the phenomenon known as 'surface seal', which typically occurs at Froude numbers Fr = V 2 0 /(gR 0 ) = O(100). As such, we are able to observe the evolution of a smooth cavity in a more extended parameter space than has been achieved in previous studies. Furthermore, by systematically varying the tank size and sphere diameter, we examine the influence of increasing wall effects on these guarded impact cavities and note the formation of surface undulations with wavelength λ = O(10) cm and acoustic waves λ a = O(D 0 ) along the cavity interface, which produce multiple pinch-off points. Acoustic waves are initiated by pressure perturbations, which themselves are generated by the primary cavity pinch-off. Using high-speed particle image velocimetry (PIV) techniques we study the bulk fluid flow for the most constrained geometry and show the larger undulations (λ = O(10 cm)) have a fixed nature with respect to the lab frame. We show that previously deduced scalings for the normalized (primary) pinch-off location (ratio of pinch-off depth to sphere depth at pinch-off time), H p /H = 1/2, and pinch-off time, τ ∝ (R 0 /g) 1/2 , do not hold for these extended cavities in the presence of strong wall effects (sphere-to-tank diameter ratio), = D 0 /D tank 1/16. Instead, we find multiple distinct regimes for values of H p /H as the observed undulations are induced above the first pinch-off point as the impact speed increases. We also report observations of 'kinked' pinch-off points and the suppression of downward facing jets in the presence of wall effects. Surprisingly, upward facing jets emanating from first cavity pinch-off points evolve into a 'flat' structure at high impact speeds, both in the presence and absence of wall effects.

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Section: Introductionmentioning

confidence: 99%

Water entry without surface seal: extended cavity formation

et al. 2014

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“…Their work, like much of the existing theoretical work done to determine the force at impact, only considers impact up to a maximum penetration depth of half a sphere diameter. May & Woodhull (1948, 1950 note that the drag coefficient declines gradually towards a value between 0.25 and 0.3 when cavity is formed; the precise shape of the curve appears to depends on the specific gravity of the impacting object.…”

Section: Water-entry Problemmentioning

confidence: 99%

“…Richardson (1948) and May & Woodhull (1948, 1950 derive force components using force balance equations and position-time curves, taken from high-speed video after the sphere is fully submerged. Kornhauser (1964) offers a review of these force models derived from experimental data.…”

Section: Water-entry Problemmentioning

confidence: 99%

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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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“…The early research on the water-entry problem mainly focused on spheres [1][2][3]. With the development of computational and testing technology, a lot of experimental and numerical research of water-entry of other shape bodies have been carried out and published.…”

Section: Introductionmentioning

confidence: 99%

Numerical Investigations of Cavitation Nose Structure of a High-Speed Projectile Impact on Water-Entry Characteristics

2020

JMSE

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In this study, a detailed analysis of the influences of cavitation nose structure of a high-speed projectile on the trajectory stability during the water-entry process was investigated numerically. The Zwart-Gerber-Belamri (Z-G-B) cavitation model and the Shear Stress Ttransport (SST)k-ω turbulence model based on the Reynolds Averaged Navier–Stokes (RANS) method were employed. The numerical methodology was validated by comparing the numerical simulation results with the experimental photograph of cavitation shape and the experimental underwater velocity. Based on the numerical methodology, the disk and the conical cavitation noses were selected to investigate the water-entry characteristics. The influences of cavitation nose angle and cavitation nose diameter of the projectile on the trajectory stability and flow characteristics were carried out in detail. The variation features of projectile trajectory, velocity attenuation and drag were conducted, respectively. In addition, the cavitation characteristics of water-entry is presented and analyzed. Results show that the trajectory stability can be improved by increasing the cavitation nose angle, but the drag reduction performance will be reduced simultaneously. Additionally, due to the weakening of drag reduction performance, the lower velocity of the projectile will cause the damage of the cavitation shape and the trajectory instability. Furthermore, the conical cavitation nose has preferable trajectory stability and drag reduction performance than the disk cavitation nose.

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The Virtual Mass of a Sphere Entering Water Vertically

Cited by 53 publications

References 3 publications

Water entry without surface seal: extended cavity formation

Water entry without surface seal: extended cavity formation

Water entry of spinning spheres

Numerical Investigations of Cavitation Nose Structure of a High-Speed Projectile Impact on Water-Entry Characteristics

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