Hostname: page-component-586b7cd67f-t7fkt Total loading time: 0 Render date: 2024-11-23T19:06:12.777Z Has data issue: false hasContentIssue false
  • English
  • Français

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: [email protected]
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Aristoff, J. M. & Bush, J. W. M. 2009 Water entry of small hydrophobic spheres. J. Fluid Mech. 619, 45–78.CrossRefGoogle Scholar
Birkhoff, G. & Zarantonello, E. H. 1957 Jets, Wakes, and Cavities. Academic Press.Google Scholar
Chu, P. C., Fan, C. W., Evans, A. D. & Gilles, A. F. 2004 Triple coordinate transforms for prediction of falling cylinder through the water column. J. Appl. Mech. 71, 292–298.CrossRefGoogle Scholar
Dommermuth, D. G. & Yue, D. K. 1987 Numerical simulations of nonlinear axisymmetric flows with a free surface. J. Fluid Mech. 178, 195–219.CrossRefGoogle Scholar
Duclaux, V., Caille, F., Duez, C., Ybert, C., Bocquet, L. & Clanet, C. 2007 Dynamics of transient cavities. J. Fluid Mech. 591, 1–19.CrossRefGoogle Scholar
Duez, C., Ybert, C., Clanet, C. & Bocquet, L. 2007 Making a splash with water repellency. Nature Phys. 3, 180–183.CrossRefGoogle Scholar
Gaudet, S. 1998 Numerical simulation of circular disks entering the free surface of a fluid. Phys. Fluids 10 (10), 2489–2499.Google Scholar
Gilbarg, D. & Anderson, R. A. 1948 Influence of atmospheric pressure on the phenomena accompanying the entry of spheres into water. J. Appl. Phys. 19 (2), 127–139.Google Scholar
Glasheen, J. W. & McMahon, T. A. 1996 Vertical water entry of disks at low Froude numbers. Phys. Fluids 8 (8), 2078–2083.CrossRefGoogle Scholar
Greenhow, M. 1988 Water-entry and -exit of a horizontal circular cylinder. Appl. Ocean Res. 10 (4), 191–198.CrossRefGoogle Scholar
Holland, K. T., Green, A. W., Abelev, A. & Valent, P. J. 2004 Parameterization of the in-water motions of falling cylinders using high-speed video. Exp. Fluids 37 (5), 690–700.CrossRefGoogle Scholar
Hulme, A. 1983 A ring source integral equation method for the calculation of hydrodynamic forces exerted on floating bodies of revolution. J. Fluid Mech. 128, 387–412.CrossRefGoogle Scholar
Kominiarczuk, J. K. 2007 Cavity and projectile dynamics in intermediate Froude number water entry. SB thesis, Massachusetts Institute of Technology, Cambridge, MA.Google Scholar
Korobkin, A. A. & Pukhnachov, V. V. 1988 Initial stage of water impact. Annu. Rev. Fluid Mech. 20, 159–185.CrossRefGoogle Scholar
Laerm, J. 1974 A functional analysis of morphological variation and differential niche utilization in basilisk lizards. Ecology 55, 404–411.CrossRefGoogle Scholar
Lee, M., Longoria, R. G. & Wilson, D. E. 1997 Cavity dynamics in high-speed water entry. Phys. Fluids 9 (3), 540–550.Google Scholar
Lin, M. C. & Shieh, L. D. 1997 Simultaneous measurements of water impact on a two-dimensional body. Fluid Dyn. Res. 19, 125–148.Google Scholar
Liu, Y., Xue, M., & Yue, D. K. 2001 Computations of fully nonlinear three-dimensional wave-wave and wave-body interactions. Part 2. Nonlinear waves and forces on a body. J. Fluid Mech. 438, 41–66.CrossRefGoogle Scholar
Lohse, D., Bergmann, R., Mikkelsen, R., Zeilstra, C., van der Meer, D., Versluis, M., van der Weele, K., van der Hoef, M. & Kuipers, H. 2004 Impact on soft sand: void collapse and jet formation. Phys. Rev. Lett. 93 (19), 198003.CrossRefGoogle ScholarPubMed
Mann, J. L. 2005 Deterministic and stochastic modeling of the water entry and descent of three-dimensional cylindrical bodies. MS thesis, Massachusetts Institute of Technology, Cambridge, MA.Google Scholar
Mann, J. L., Liu, Y., Kim, Y. & Yue, D. K. P. 2007 Deterministic and stochastic predictions of motion dynamics of cylindrical mines falling through water. IEEE J. Ocean Engng 32 (1), 21–33.Google Scholar
May, A. 1951 Effect of surface condition of a sphere on its water-entry cavity. J. Appl. Phys. 22 (10), 1219–1222.CrossRefGoogle Scholar
May, A. 1952 Vertical entry of missiles into water. J. Appl. Phys. 23 (12), 1362–1372.Google Scholar
May, A. & Woodhull, J. C. 1948 Drag coefficients of steel spheres entering the water vertically. J. Appl. Phys. 19, 1109–1121.Google Scholar
Mei, C. C., Stiassnie, M., & Yue, D. K. 2005 Theory and Applications of Ocean Surface Waves, Part 1: Linear Aspects. World Scientific.Google Scholar
Newman, J. N. 1977 Marine Hydrodynamics. MIT Press.CrossRefGoogle Scholar
Richardson, E. G. 1948 The impact of a solid on a liquid surface. Proc. Phys. Soc. 61, 352–367.Google Scholar
Truscott, T. T. & Techet, A. H. 2009 Water-entry of spinning spheres. J. Fluid Mech. 625, 135–165.Google Scholar
Van Dyke, M. 1964 Perturbation Methods in Fluid Mechanics. Academic Press.Google Scholar
Wang, Q. X. 2004 Numerical simulation of violent bubble motion. Phys. Fluids 16 (5), 1610–1619.Google Scholar
Wang, Q. X. 2005 Analyses of a slender body moving near a curved ground. Phys. Fluids 17 (9), 097102.CrossRefGoogle Scholar
Wang, Q. X. 2007 An analytical solution for two slender bodies of revolution translating in very close proximity. J. Fluid Mech. 582, 223–251.Google Scholar
Worthington, A. M. & Cole, R. S. 1900 Impact with a liquid surface studied by the aid of instantaneous photography. Paper II. Phil. Trans. R. Soc. Lond. A 194, 175–199.Google Scholar
Xue, M. & Yue, D. K. 1998 Nonlinear free-surface flow due to an impulsively started submerged point sink. J. Fluid Mech. 364, 325–347.CrossRefGoogle Scholar