Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-28T02:06:45.804Z Has data issue: false hasContentIssue false
  • English
  • Français

Unsteady forces on spheres during free-surface water entry

Published online by Cambridge University Press:  02 July 2012

Tadd T. Truscott ,
Brenden P. Epps  and
Alexandra H. Techet
Tadd T. Truscott*
Affiliation:
Brigham Young University, Provo, UT 84604, USA
Brenden P. Epps
Affiliation:
Massachusetts Institute of Technology, Cambridge, MA 02139, USA
Alexandra H. Techet
Affiliation:
Massachusetts Institute of Technology, Cambridge, MA 02139, USA
*
†Email address for correspondence: truscott@byu.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

We present a study of the forces during free-surface water entry of spheres of varying masses, diameters, and surface treatments. Previous studies have shown that the formation of a subsurface air cavity by a falling sphere is conditional upon impact speed and surface treatment. This study focuses on the forces experienced by the sphere in both cavity-forming and non-cavity-forming cases. Unsteady force estimates require accurate determination of the deceleration for both high and low mass ratios, especially as inertial and hydrodynamic effects approach equality. Using high-speed imaging, high-speed particle image velocimetry, and numerical simulation, we examine the nature of the forces in each case. The effect of mass ratio is shown, where a lighter sphere undergoes larger decelerations and more dramatic trajectory changes. In the non-cavity-forming cases, the forces are modulated by the growth and shedding of a strong, ring-like vortex structure. In the cavity-forming cases, little vorticity is shed by the sphere, and the forces are modulated by the unsteady pressure required for the opening and closing of the air cavity. A data-driven boundary-element-type method is developed to accurately describe the unsteady forces using cavity shape data from experiments.

JFM classification

Mathematical Foundations: Computational methods Vortex Flows: Vortex shedding
Type
Papers
Information
Journal of Fluid Mechanics , Volume 704 , 10 August 2012 , pp. 173 - 210
Copyright
Copyright © Cambridge University Press 2012

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

1. Abramowitz, M. & Stegun, I. A. 1972 Handbook of Mathematical Functions. Dover.Google Scholar
2. Aristoff, J. M. & Bush, J. W. M. 2009 Water entry of small hydrophobic spheres. J. Fluid Mech. 619, 45–78.CrossRefGoogle Scholar
3. Aristoff, J. M., Truscott, T. T., Techet, A. H. & Bush, J. W. M. 2010 The water entry of decelerating spheres. Phys. Fluids 22 (032102).Google Scholar
4. Asfar, K. & Moore, S. 1987 Rigid-body water impact at shallow angles of incidence. In Proceedings of the Sixth International Offshore Mechanics and Arctic Engineering Symposium, pp. 105–112. ASME, Virginia Polytechnic Inst. State Univ., Blacksburg, VA, USA.Google Scholar
5. Bergmann, R., van der Meer, D., Gekle, S., van der Bos, A. & Lohse, D. 2009 Controlled impact of a disk on a water surface: cavity dynamics. J. Fluid Mech. 633, 381–409.CrossRefGoogle Scholar
6. Birkhoff, G. & Isaacs, R. 1951 Transient cavities in air–water entry. Tech. Rep. 1490. Navord Rep.Google Scholar
7. de Boor, C. 1978 A Practical Guide to Splines. Springer.CrossRefGoogle Scholar
8. Cleveland, W. S. 1979 Robust locally weighted regression and smoothing scatterplots. J. Am. Stat. Assoc. 74 (367), 829–836.Google Scholar
9. Do-Quang, M. & Amberg, G. 2009 The splash of a solid sphere impacting on a liquid surface: numerical simulation of the influence of wetting. Phys. Fluids 21 (2), 022102.Google Scholar
10. Duclaux, V., Caillé, F., Duez, C., Ybert, C., Bocquet, L. & Clanet, C. 2007 Dynamics of transient cavities. J. Fluid Mech. 591, 1–19.Google Scholar
11. Duez, C., Ybert, C., Clanet, C. & Bocquet, L. 2007 Making a splash with water repellency. Nat. Phys. 3, 180–183.Google Scholar
12. Eggers, J., Fontelos, M. A., Leppinen, D. & Snoeijer, J. H. 2007 Theory of collapsing axisymmetric cavity. Phys. Rev. Lett. 094502.Google Scholar
13. Epps, B. P. 2010 An impulse framework for hydrodynamic force analysis: fish propulsion, water entry of spheres, and marine propellers. PhD thesis, Massachusetts Institute of Technology, Cambridge, MA.Google Scholar
14. Epps, B. P. & Techet, A. H. 2007 Impulse generated during unsteady maneuvering of swimming fish. Exp. Fluids 43 (5), 691–700.Google Scholar
15. Epps, B. P., Truscott, T. T. & Techet, A. H. 2010 Evaluating derivatives of experimental data using smoothing splines. In Proceedings of Mathematical Methods in Engineering International Symposium. MMEI, Lisbon Portugal.Google Scholar
16. Gaudet, S. 1998 Numerical simulation of circular disks entering the free surface of a fluid. Phys. Fluids 10 (10), 2489–2499.CrossRefGoogle Scholar
17. Gekle, S., Gordillo, J. M., van der Meer, D. & Lohse, D. 2009 High-speed jet formation after solid object impact. Phys. Rev. Lett. 102, 034502.Google Scholar
18. Gekle, S., Peters, I. R., Gordillo, J. M., Meer, D. & Lohse, D. 2010 Supersonic air flow due to solid–liquid impact. Phys. Rev. Lett. 104, 024501.CrossRefGoogle ScholarPubMed
19. Gharib, M., Rambod, E. & Shariff, K. 1998 A universal time scale for vortex ring formation. J. Fluid Mech. 360, 121–140.Google Scholar
20. 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
21. Glasheen, J. W. & McMahon, T. A. 1996 Vertical water entry of disks at low Froude numbers. Phys. Fluids 8 (8), 2078–2083.Google Scholar
22. Goldman, D. I. & Umbanhowar, P. 2008 Scaling and dynamics of sphere and disk impact into granular media. Phys. Rev. E 77, 021308.CrossRefGoogle ScholarPubMed
23. Gordillo, J. M. 2008 Axisymmetric bubble collapse in a quiescent liquid pool. I. Theory and numerical simulations. Phys. Fluids 20, 112103.Google Scholar
24. 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
25. Horowitz, M. & Williamson, C. H. K. 2008 Critical mass and a new periodic four-ring vortex wake mode for freely rising and falling spheres. Phys. Fluids 20, 101701.Google Scholar
26. von Kármán, 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, Washington, D.C., USA.Google Scholar
27. Korobkin, A. A. & Pukhnachov, V. V. 1988 Initial stage of water impact. Annu. Rev. Fluid Mech. 20, 159–185.Google Scholar
28. Lee, M., Longoria, R. G. & Wilson, D. E. 1997 Cavity dynamics in high-speed water entry. Phys. Fluids 9, 540–550.Google Scholar
29. May, A. & Hoover, W. R. 1963 A study of the water-entry cavity. Unclassified NOLTR 63–264. United States Naval Ordinance Laboratory, White Oak, Maryland, USA.Google Scholar
30. Milne-Thomson, L. M. 1968 Theoretical Hydrodynamics, 5th edn. Dover.Google Scholar
31. 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. 108 (1), 133–146.Google Scholar
32. Newman, J. N. 1977 Marine Hydrodynamics. MIT.Google Scholar
33. Raffel, M., Willert, C., Willert, C. E. & Kompenhans, S. 1998 Particle Image Velocimetry. Springer.Google Scholar
34. Saffman, P. 1995 Vortex Dynamics. Cabridge University Press.Google Scholar
35. Techet, A. H. & Truscott, T. T. 2011 Water entry of spinning hydrophobic and hydrophilic spheres. J. Fluids Struct. 27 (5–6), 716–726.Google Scholar
36. Thoroddsen, S. T., Etoh, T. G., Takehara, K. & Takano, Y. 2004 Impact jetting by a solid sphere. J. Fluid Mech. 499, 139–148.Google Scholar
37. Truscott, T. T. 2009 Cavity dynamics of water entry for spheres and ballistic projectiles. PhD thesis, Massachusetts Institute of Technology, Cambridge, MA, USA.Google Scholar
38. Truscott, T. T. & Techet, A. H. 2009a A spin on cavity formation during water entry of hydrophobic and hydrophilic spheres. Phys. Fluids 21, 121703.Google Scholar
39. Truscott, T. T. & Techet, A. H. 2009b Water entry of spinning spheres. J. Fluid Mech. 623, 135–165.Google Scholar
40. Wagner, H. 1932 Phenomena associated with impacts and sliding on liquid surfaces. Z. Angew. Math. Mech. 12, 193–235.CrossRefGoogle Scholar
41. Worthington, A. M. 1908 A Study of Splashes. Printed by William Brendon and Son, Ltd; reprinted by Macmillian Co., New York, 1963 edn. Longmans Green and Co., Plymouth..Google Scholar
42. Yan, H., Liu, Y., Kominiarczuk, J. & Yue, D. P. 2009 Cavity dynamics in water entry at low Froude numbers. J. Fluid Mech. 641, 441–461.Google Scholar