Water Entry and the Cavity-Running Behavior of Missiles

May, Albert

doi:10.21236/ada020429

Cited by 142 publications

(63 citation statements)

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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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“…Subsequent early impact studies typically focus on ballistics investigations in military laboratories. The experiments of May (1975) are some of the most extensive studies of free surface impact for naval ordinance applications. His research focuses on the formation of the air cavity in the wake of spherical projectiles with high-impact velocities.…”

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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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“…In the super cavity model the following assumptions are (see [1]): -The motion of the projectile is confined to a plane; -The slender body rotates about its nose; -The effect of gravity on the dynamics of this body is negligible; -The motion of the slender body is not influenced by the presence of gas, water vapor or water drops in the cavity; The super cavity problems are studied in ( [1][2][3][4][5][6][7][8]). The Data Assimilation method using differential variation is based on the theory of optimal control for partial differential equation (Lions, 1971 see [9][10][11]).…”

Section: Introductionmentioning

confidence: 99%