Hostname: page-component-8448b6f56d-sxzjt Total loading time: 0 Render date: 2024-04-23T07:37:42.108Z Has data issue: false hasContentIssue false
  • English
  • Français

Water entry of spinning spheres

Published online by Cambridge University Press:  14 April 2009

TADD T. TRUSCOTT  and
ALEXANDRA H. TECHET
TADD T. TRUSCOTT
Affiliation:
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
ALEXANDRA H. TECHET*
Affiliation:
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
*
†Email address for correspondence: ahtechet@MIT.EDU
Get access Rights & Permissions [Opens in a new window]

Abstract

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.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 625 , 25 April 2009 , pp. 135 - 165
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

Abelson, H. I. 1970 Pressure measurements in the water-entry cavity. J. Fluid Mech. 44, 129–144.CrossRefGoogle Scholar
Alaways, L. W. & Hubbard, M. 2001 Experimental determination of baseball spin and lift. J. Sports Sci. 19, 349–358.CrossRefGoogle ScholarPubMed
Barkla, H. M. & Auchterlonie, L. J. 1971 The Magnus or Robins effect on rotating spheres. J. Fluid Mech. 47, 437–447.CrossRefGoogle Scholar
Bearman, P. W. & Harvey, J. K. 1976 Golf ball aerodynamics. Aeronaut. Q. 27, 112–122.CrossRefGoogle Scholar
Bell, G. E. 1924 On the impact of a solid sphere with a fluid surface. Phil. Mag. 48, 753–764.CrossRefGoogle Scholar
Bergmann, R., van der Meer, D., Stijnman, M., Sandtke, M., Prosperetti, A. & Lohse, D. 2006 Giant bubble pinch-off. Phys. Rev. Lett. 96, 154505–4.CrossRefGoogle ScholarPubMed
Birkhoff, G. & Isaacs, R. 1951 Transient cavities in air–water entry. NAVORD Report No. 1490.Google Scholar
Blevins, R. D. 1984 Applied Fluid Dyanmics Handbook. Van Nostrand Reinhold Co.Google Scholar
Davies, J. M. 1949 The aerodynamics of golf balls. J. Appl. Phys. 20, 821–828.CrossRefGoogle Scholar
Duez, C., Ybert, C., Clanet, C. & Bocquet, L. 2007 Making a splash with water repellency. Nat. Phys. 3, 180–183.CrossRefGoogle Scholar
Gaudet, S. 1998 Numerical simulation of circular disks entering the free surface of a fluid. Phy. Fluids 10, 2489–2499.CrossRefGoogle 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, 127–139.CrossRefGoogle Scholar
Glasheen, J. W. & McMahon, T. A. 1996 Vertical water entry of disks at low Froude numbers. Phys. Fluids 8, 2078–2083.CrossRefGoogle Scholar
Govardhan, R. & Williamson, C. 2005 Vortex-induced vibrations of a sphere. J. Fluid Mech. 531, 11–47.CrossRefGoogle Scholar
Grumstrup, T., Keller, J. B. & Belmonte, A. 2007 Cavity ripples observed during the impact of solid objects into liquids. Phys. Rev. Lett. 99, 114502.CrossRefGoogle ScholarPubMed
von Karman, T. 1929 The impact on seaplane floats during landing. Technical Notes 321. National Advisory Committee for Aeronautics, Aerodynamic Institute of the Technical High School, Aachen.Google Scholar
Kornhauser, M. 1964 Structural Effects of Impact, Spartan Books, Inc., Baltimore, MD.Google Scholar
Lee, M., Longoria, R. G. & Wilson, D. E. 1997 Cavity dynamics in high-speed water entry. Phys. Fluids 9, 540.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, 198003.CrossRefGoogle ScholarPubMed
Maccoll, J. W. 1928 Aerodynamics of a spinning sphere. J. R. Aeronaut. Soc. 32 (213), 777–798.CrossRefGoogle Scholar
May, A. 1951 Effect of surface condition of a sphere on its water-entry cavity. J. Appl. Phys. 22, 1219–1222.CrossRefGoogle Scholar
May, A. 1952 Vertical entry of missiles into water. J. Appl. Phys. 23, 1362–1372.CrossRefGoogle Scholar
May, A. 1975 Water entry and the cavity-running behaviour of missiles. Final. Naval Surface Weapons Center White Oak Laboratory, Silver Springs, MD.CrossRefGoogle Scholar
May, A. & Hoover, W. R. 1963 A study of the water-entry cavity. Unclassified NOLTR 63-264. United States Naval Ordinance Laboratory, White Oak, MD.CrossRefGoogle Scholar
May, A. & Woodhull, J. C. 1948 Drag coefficients of steel spheres entering water vertically. J. Appl. Phys. 19, 1109–1121.CrossRefGoogle Scholar
May, A. & Woodhull, J. C. 1950 The virtual mass of a sphere entering water vertically. J. App. Phys. 21, 1285–1289.CrossRefGoogle Scholar
Mehta, R. D. 1985 Aerodynamics of sports balls. Annu. Rev. Fluid Mech. 17, 151–189.CrossRefGoogle Scholar
Moghisi, M. & Squire, P. T. 1981 An experimental investigation of the initial force of impact on a sphere striking a liquid surface. J. Fluid Mech. Digital Arch. 108, 133–146.CrossRefGoogle Scholar
Newton, I. 1671 New theory about light and colors. Phil. Trans. R. Soc. 6, 3078.Google Scholar
Raffel, M., Willert, C., Willert, C. E. & Kompenhans, S. 1998 Particle Image Velocimetry. Springer.CrossRefGoogle Scholar
Richardson, E. G. 1948 The impact of a solid on a liquid surface. Proc. Phys. Soc. 4, 352–367.CrossRefGoogle Scholar
Robbins, B. 1742 New Principles of Gunnery. Richmond (republished by Richmond in 1972, first printed by ed. Hutton, A).Google Scholar
Rosellini, L., Hersen, F., Clanet, C. & Bocquet, L. 2005 Skipping stones. J. Fluid Mech. 543, 137–146.CrossRefGoogle Scholar
Shi, H.-H., Itoh, M. & Takami, T. 2000 Optical observation of the supercavitation induced by high-speed water entry. J. Fluids Engng 122 (4), 806–810.CrossRefGoogle Scholar
Smits, A. J. & Smith, D. R. 1994 A New Aerodynamic Model of a Golf Ball in Flight. E. and F. N. Spon.Google Scholar
Thoroddsen, S. T. 2002 The ejecta sheet generated by the impact of a drop. J. Fluid Mech. 451, 373–381.CrossRefGoogle Scholar
Thoroddsen, S. T., Etoh, T. G., Takehara, K. & Takano, Y. 2004 Impact jetting by a solid sphere. J. Fluid Mech. 499, 139–148.CrossRefGoogle Scholar
Truscott, T. T. & Techet, A. H. 2006 Cavity formation in the wake of a spinning sphere impacting the free surface. Phys. Fluids 18, 091113.CrossRefGoogle Scholar
Watts, R. G. & Ferrer, R. 1987 The lateral force on a spinning sphere: aerodynamics of a curveball. Am. J. Phys. 55, 40–44.CrossRefGoogle Scholar
Worthington, A. M. & Cole, R. S. 1897 Impact with a liquid surface, studied by the aid of instantaneous photography. Phil. Trans. R. Soc. Lond. Ser. A (Containing Papers of a Mathematical or Physical Character) 189, 137–148.Google Scholar
Yarin, A. L. 2006 Drop impact dynamics: splashing, spreading, receding, bouncing. Annu. Rev. Fluid Mech. 38, 159–192.CrossRefGoogle Scholar
Zhao, R. & Faltinsen, O. M. 1993 Water entry of two-dimensional bodies. J. Fluid Mech. 246, 593–612.CrossRefGoogle Scholar