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Cavity dynamics in water entry at low Froude numbers

Published online by Cambridge University Press:  30 November 2009

HONGMEI YAN ,
YUMING LIU ,
JAKUB KOMINIARCZUK  and
DICK K. P. YUE
HONGMEI YAN
Affiliation:
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
YUMING LIU
Affiliation:
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
JAKUB KOMINIARCZUK
Affiliation:
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
DICK K. P. YUE*
Affiliation:
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
*
†Email address for correspondence: yue@mit.edu
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Abstract

The dynamics of the air cavity created by vertical water entry of a three-dimensional body is investigated theoretically, computationally and experimentally. The study is focused in the range of relatively low Froude numbers, Fr ≡ V(gD)−1/2 ≤ O(10) (where V is the dropping velocity of the body, D its characteristic dimension and g the gravitational acceleration), when the inertia and gravity effects are comparable. To understand the physical processes involved in the evolution of cavity, we conduct laboratory experiments of water entry of freely dropping spheres. A matched asymptotic theory for the description of the cavity dynamics is developed based on the slender-body theory in the context of potential flow. Direct comparisons with experimental data show that the asymptotic theory properly captures the key physical effects involved in the development of the cavity, and in particular gives a reasonable prediction of the maximum size of the cavity and the time of cavity closure. Due to the inherent assumption in the asymptotic theory, it is incapable of accurately predicting the flow details near the free surface and the body, where nonlinear free surface and body boundary effects are important. To complement the asymptotic theory, a fully nonlinear numerical study using an axisymmetric boundary integral equation is performed. The numerically obtained dependencies of the cavity height and closure time on Froude number and body geometry are in excellent agreement with available experiments.

JFM classification

Drops and Bubbles: Bubble dynamics
Type
Papers
Information
Journal of Fluid Mechanics , Volume 641 , 25 December 2009 , pp. 441 - 461
Copyright
Copyright © Cambridge University Press 2009

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