Skip to main content
SpringerLink
Log in

A study of energy transfer during water entry of solids using incompressible SPH simulations

  • Published:
Sādhanā Aims and scope Submit manuscript

Abstract

Cavity formation during water entry of a solid corresponds to the deceleration experienced by the solid. Several experimental studies in the past have facilitated qualitative understanding of the relation between flow and impact properties and the type of cavity formed. The types of cavities formed are classified primarily based on the nature of the seal, such as (a) surface seal, (b) deep seal, (c) shallow seal and (d) quasi-static seal. The flow mechanism behind these features and their effects on the speed of the impacting solid require further quantitative understanding. A study of such phenomenon is difficult using the existing CFD techniques owing to the fact that the high density ratios between the two phases, namely water and air, bring in issues with respect to the convergence of the linear system used to solve for the pressure field for a divergence-free velocity field. Based on a free surface modeling method, we present Incompressible Smoothed Particle Hydrodynamics (ISPH) simulations of water entry of two-dimensional solids of different shapes, densities and initial angular momenta. From the velocity field of the fluid and shape of the cavity, we relate the transfer of kinetic energy from the solid to the fluid through different phases of the cavity formation. Finally, we present a three-dimensional simulation of water entry to assert the utility of the method for analysis of real life water entry scenarios.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6
Figure 7
Figure 8
Figure 9
Figure 10
Figure 11
Figure 12
Figure 13
Figure 14
Figure 15
Figure 16
Figure 17
Figure 18
Figure 19
Figure 20

Similar content being viewed by others

References

  1. Yan H, Liu Y, Kominiarczuk J and Yue D K P 2009 Cavity dynamics in water entry at low froude numbers. J. Fluid Mech. 641: 441–461

    Article  MATH  Google Scholar 

  2. Worthington A M and Cole R S 1897 Impact with a liquid surface, studied by the aid of instantaneous photography. Philos. Trans. R. Soc. A 189: 137–148

    Article  MATH  Google Scholar 

  3. Gilbarg D and 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

    Article  Google Scholar 

  4. May A and Woodhull J C 1948 Drag coefficients of steel spheres entering water vertically. J. Appl. Phys. 19(12): 1109–1121

    Article  Google Scholar 

  5. May A 1951 Effect of surface condition of a sphere on its water-entry cavity. J. Appl. Phys. 22(10): 1219–1222

    Article  Google Scholar 

  6. May A 1952 Vertical entry of missiles into water. J. Appl. Phys. 23(12): 1362–1372

    Article  Google Scholar 

  7. Richardson E G 1948 The impact of a solid on a liquid surface. Proc. Phys. Soc. 61(4): 352

    Article  MathSciNet  Google Scholar 

  8. Glasheen J W and McMahon T A 1996 A hydrodynamic model of locomotion in the basilisk lizard. Nature 380(6572): 340–341

    Article  Google Scholar 

  9. Holland K T, Green A W, Abelev A and Valent P J 2004 Parameterization of the in-water motions of falling cylinders using high-speed video. Exp. Fluids 37(5): 690–700

    Article  Google Scholar 

  10. Chu P C, Fan C, Evans A D and Gilles A 2004 Triple coordinate transforms for prediction of falling cylinder through the water column. J. Appl. Mech. 71(2): 292–298

    Article  MATH  Google Scholar 

  11. Truscott T T, Epps B P and Belden J 2014 Water entry of projectiles. Annu. Rev. Fluid Mech. 46: 355–378

    Article  MathSciNet  MATH  Google Scholar 

  12. Techet A H and Truscott T T 2011 Water entry of spinning hydrophobic and hydrophilic spheres. J. Fluid. Struct. 27(5): 716–726

    Article  Google Scholar 

  13. Truscott T T and Techet A H 2006 Cavity formation in the wake of a spinning sphere impacting the free surface. Phys. Fluids 18(9): 91113–91113

    Article  Google Scholar 

  14. Truscott T T and Techet A H 2009 A spin on cavity formation during water entry of hydrophobic and hydrophilic spheres. Phys. Fluids 21(12): 121703

    Article  MATH  Google Scholar 

  15. Truscott T, Belden J and Hurd R 2014 Water-skipping stones and spheres. Phys. Today 67(12): 70–71

    Article  Google Scholar 

  16. Birkhoff G et al 2012 Jets, wakes, and cavities. Elsevier, Amsterdam

  17. Ahmadzadeh M, Saranjam B, Hoseini Fard A and Binesh A R 2014 Numerical simulation of sphere water entry problem using Eulerian–Lagrangian method. Appl. Math. Model. 38(5–6): 1673–1684

    Article  MathSciNet  Google Scholar 

  18. Gingold R A and Monaghan J J 1977 Smoothed particle hydrodynamics – theory and application to non-spherical stars. Mon. Not. R. Astron. Soc. 181: 375–389

    Article  MATH  Google Scholar 

  19. Monaghan J 1985 Particle methods for hydrodynamics. Comput. Phys. Rep. 3(2): 71–124

    Article  Google Scholar 

  20. Monaghan J J 2005 Smoothed particle hydrodynamics. Rep. Prog. Phys. 68(8): 1703

    Article  MathSciNet  MATH  Google Scholar 

  21. Cummins S J and Rudman M 1999 An SPH projection method. J. Comput. Phys. 152(2): 584–607

    Article  MathSciNet  MATH  Google Scholar 

  22. Nair P and Tomar G 2015 Volume conservation issues in incompressible smoothed particle hydrodynamics. J. Comput. Phys. 297: 689–699

    Article  MathSciNet  MATH  Google Scholar 

  23. Nair P and Tomar G 2014 An improved free surface modeling for incompressible SPH. Comput. Fluids 102: 304–314

    Article  MathSciNet  Google Scholar 

  24. Greenhow M and Lin W-M 1983 Nonlinear-free surface effects: experiments and theory. Technical Report, DTIC Document

    Google Scholar 

  25. Truscott T T and Techet A H 2009 Water entry of spinning spheres. J. Fluid. Mech. 625: 135–165

    Article  MATH  Google Scholar 

  26. Aristoff J M, Truscott T T, Techet A H, and Bush J W M 2010 The water entry of decelerating spheres. Phys. Fluids 22(3): 032102

    Article  MATH  Google Scholar 

  27. Antuono M, Colagrossi A, Le Touzé D and Monaghan J J 2013 Conservation of circulation in SPH for 2D free-surface flows. Int. J. Numer. Methods Fluids 72(5): 583–606

    Article  MathSciNet  Google Scholar 

  28. Dehnen W and Aly H 2012 Improving convergence in smoothed particle hydrodynamics simulations without pairing instability. Mon. Not. R. Astron. Soc. 425(2): 1068–1082

    Article  Google Scholar 

  29. Colagrossi A, Souto-Iglesias A, Antuono M and Marrone S 2013 Smoothed-particle-hydrodynamics modeling of dissipation mechanisms in gravity waves. Phys. Rev. E 87(2): 023302

    Article  Google Scholar 

  30. Monaghan J J 1994 Simulating free surface flows with SPH. J. Comput. Phys. 110(2): 399–406

    Article  MathSciNet  MATH  Google Scholar 

  31. Cole R H 1948 Underwater explosions. Princeton, NJ: Princeton University Press

    Book  Google Scholar 

  32. Lee E S, Moulinec C, Xu R, Violeau D, Laurence D and Stansby P 2008 Comparisons of weakly compressible and truly incompressible algorithms for the SPH mesh free particle method. J. Comput. Phys. 227(18): 8417–8436

    Article  MathSciNet  MATH  Google Scholar 

  33. Nishida A 2010 Experience in developing an open source scalable software infrastructure in Japan. In: Proceedings of Computational Science and Its Applications–ICCSA 2010, p. 448–462. Springer, Berlin

  34. Shao S and Lo E Y M 2003 Incompressible SPH method for simulating Newtonian and non-Newtonian flows with a free surface. Adv. Water Resour. 26: 787–800

    Article  Google Scholar 

  35. Khayyer A, Gotoh H and Shao S D 2008 Corrected incompressible SPH method for accurate water-surface tracking in breaking waves. Coast. Eng. 55: 236–250

    Article  Google Scholar 

  36. Rafiee A and Thiagarajan K P 2009 An SPH projection method for simulating fluid–hypoelastic structure interaction. Comput. Method. Appl. Mech. Eng. 198(33–36): 2785–2795

    Article  MATH  Google Scholar 

  37. Gotoh H and Sakai T 2006 Key issues in the particle method for computation of wave breaking. Coast. Eng. 53(2): 171–179

    Article  Google Scholar 

  38. Koshizuka S, Nobe A and Oka Y 1998 Numerical analysis of breaking waves using the moving particle semi-implicit method. Int. J. Numer. Methods Fluids, 26: 751–769

    Article  MATH  Google Scholar 

  39. Bøckmann A, Shipilova O and Skeie G 2012 Incompressible SPH for free surface flows. Comput. Fluids 67: 138–151

    Article  MathSciNet  Google Scholar 

  40. von Kármán T 1929 The impact on seaplane floats during landing. National Advisory Committee on Aeronautics

  41. Hoover W R and Dawson V C D 1966 Hydrodynamic pressure measurements of the vertical water entry of a sphere. Technical Report, DTIC Document

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, Indian Institute of Science, Bangalore, 560012, India

    Prapanch Nair & Gaurav Tomar

Authors
  1. Prapanch Nair
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Gaurav Tomar
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Prapanch Nair.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Nair, P., Tomar, G. A study of energy transfer during water entry of solids using incompressible SPH simulations. Sādhanā 42, 517–531 (2017). https://doi.org/10.1007/s12046-017-0615-y

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12046-017-0615-y

Keywords

Search

Navigation