Skip to main content
Log in

Numerical simulation of water entry of a wedge using a modified ghost-cell immersed boundary method

  • Original article
  • Published:
Journal of Marine Science and Technology Aims and scope Submit manuscript

Abstract

The hydrodynamic problems of water entry of a wedge are investigated by a modified ghost-cell immersed boundary method. The modifications correspond to a newly proposed scheme for dealing with fluid–body interaction, and incorporation of CIP (Constraint Interpolation Profile) method and THINC/SW (Tangent of Hyperbola for Interface Capturing with Slope Weighting) method. The modified ghost-cell immersed boundary method uses a compact interpolation structure and gives the fluid properties to the ghost cell to achieve a more accurate treatment of fluid–body interaction. It can preserve the sharpness of the immersed boundary. To validate the new method, simulations of water entry of symmetric and asymmetric wedges in a single degree of freedom and water entry of an asymmetric wedge in three degrees of freedom are carried out, respectively. The variations of pressure, vertical velocity, vertical acceleration, angular displacement, and angular acceleration against time are focused on. The evolution of the free surface and velocity distributions of fluid is also analyzed. The results of numerical simulations are compared with available experimental results and fairly good agreement is obtained, which indicates that the present model is reliable.

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

Access this article

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

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23

Similar content being viewed by others

References

  1. Faltinsen OM (2000) Hydroelastic slamming. J Mar Sci Technol 5:49–65. https://doi.org/10.1007/s007730070011

    Article  Google Scholar 

  2. Seddon C, Moatamedi M (2006) Review of water entry with applications to aerospace structures. Int J Impact Eng 32:1045–1067. https://doi.org/10.1016/j.ijimpeng.2004.09.002

    Article  Google Scholar 

  3. Jiang Y, Bai T, Gao Y, Guan L (2018) Water entry of a constraint posture body under different entry angles and ventilation rates. Ocean Eng 153:53–59. https://doi.org/10.1016/j.oceaneng.2018.01.091

    Article  Google Scholar 

  4. Wei Z, Hu C (2015) Experimental study on water entry of circular cylinders with inclined angles. J Mar Sci Technol 20:722–738. https://doi.org/10.1007/s00773-015-0326-1

    Article  Google Scholar 

  5. Zou L, Wang A, Wang Z, Pei Y, Liu X (2019) Experimental study of freak waves due to three-dimensional island terrain in random wave. Acta Oceanol Sin 38:1–8. https://doi.org/10.1007/s13131-019-1390-x

    Article  Google Scholar 

  6. Hu Z, Zhao X, Li M, Fang Z, Sun Z (2018) A numerical study of water entry of asymmetric wedges using a cip-based model. Ocean Eng 148:1–16. https://doi.org/10.1016/j.oceaneng.2017.11.011

    Article  Google Scholar 

  7. Yang L, Yang H, Yan S, Ma Q, Bihnam M et al (2016) Comparative study on water impact problem. In: The 26th international ocean and polar engineering conference, international society of offshore and polar engineers

  8. Peskin CS (2002) The immersed boundary method. Acta Num 11:479–C517. https://doi.org/10.1017/S0962492902000077

    Article  MathSciNet  MATH  Google Scholar 

  9. Von Kármán T (1929) The impact of seaplane floats during landing. Nat Adv Com Aeronautics Tech Note 321:309–313

    Google Scholar 

  10. Wagner H (1932) Über stoß-und gleitvorgänge an der oberfläche von flüssigkeiten. ZAMM J Appl Math Mech 12:193–215. https://doi.org/10.1002/zamm.19320120402

    Article  MATH  Google Scholar 

  11. Yu P, Li H, Ong MC (2019) Hydroelastic analysis on water entry of a constant-velocity wedge with stiffened panels. Mar Struct 63:215–238. https://doi.org/10.1016/j.marstruc.2018.09.007

    Article  Google Scholar 

  12. Sun P, Zhang A, Marrone S, Ming F (2018) An accurate and efficient sph modeling of the water entry of circular cylinders. Appl Ocean Res 72:60–75. https://doi.org/10.1016/j.apor.2018.01.004

    Article  Google Scholar 

  13. Yettou EM, Desrochers A, Champoux Y (2006) Experimental study on the water impact of a symmetrical wedge. Fluid Dyn Res 38:47–66. https://doi.org/10.1016/j.fluiddyn.2005.09.003

    Article  MATH  Google Scholar 

  14. Tveitnes T, Fairlie-Clarke A, Varyani K (2008) An experimental investigation into the constant velocity water entry of wedge-shaped sections. Ocean Eng 35:1463–1478. https://doi.org/10.1016/j.oceaneng.2008.06.012

    Article  Google Scholar 

  15. De Backer G, Vantorre M, Beels C, De Pré J, Victor S, De Rouck J, Blommaert C, Van Paepegem W (2009) Experimental investigation of water impact on axisymmetric bodies. Appl Ocean Res 31:143–156. https://doi.org/10.1016/j.apor.2009.07.003

    Article  Google Scholar 

  16. Jalalisendi M, Osma SJ, Porfiri M (2015) Three-dimensional water entry of a solid body: a particle image velocimetry study. J Fluids Struct 59:85–102

    Article  Google Scholar 

  17. Russo S, Jalalisendi M, Falcucci G, Porfiri M (2018) Experimental characterization of oblique and asymmetric water entry. Exp Thermal Fluid Sci 92:141–161. https://doi.org/10.1016/j.expthermflusci.2017.10.028

    Article  Google Scholar 

  18. Zhao R, Faltinsen O (1993) Water entry of two-dimensional bodies. J Fluid Mech 246:593–612. https://doi.org/10.1017/S002211209300028X

    Article  MATH  Google Scholar 

  19. Wu G, Sun H, He Y (2004) Numerical simulation and experimental study of water entry of a wedge in free fall motion. J Fluids Struct 19:277–289. https://doi.org/10.1016/j.jfluidstructs.2004.01.001

    Article  Google Scholar 

  20. Gong K, Liu H, Wang Bl (2009) Water entry of a wedge based on sph model with an improved boundary treatment. J Hydrodyn 21:750–757. https://doi.org/10.1016/S1001-6058(08)60209-7

    Article  Google Scholar 

  21. Shao S (2009) Incompressible sph simulation of water entry of a free-falling object. Int J Num Methods Fluids 59:91–115. https://doi.org/10.1002/fld.1813

    Article  MathSciNet  MATH  Google Scholar 

  22. Shao J, Yang Y, Gong H, Liu M (2019) Numerical simulation of water entry with improved sph method. Int J Comput Methods 16:1846004. https://doi.org/10.1142/S0219876218460040

    Article  MathSciNet  MATH  Google Scholar 

  23. Zhu L, Peskin CS (2003) Interaction of two flapping filaments in a flowing soap film. Phys Fluids 15:1954–1960. https://doi.org/10.1063/1.1582476

    Article  MathSciNet  MATH  Google Scholar 

  24. Su SW, Lai MC, Lin CA (2007) An immersed boundary technique for simulating complex flows with rigid boundary. Comput Fluids 36:313–324. https://doi.org/10.1016/j.compfluid.2005.09.004

    Article  MATH  Google Scholar 

  25. Balaras E (2004) Modeling complex boundaries using an external force field on fixed cartesian grids in large-eddy simulations. Comput Fluids 33:375–404. https://doi.org/10.1016/S0045-7930(03)00058-6

    Article  MATH  Google Scholar 

  26. Zhang N, Zheng ZC (2007) An improved direct-forcing immersed-boundary method for finite difference applications. J Comput Phys 221:250–268. https://doi.org/10.1016/j.jcp.2006.06.012

    Article  MathSciNet  MATH  Google Scholar 

  27. Mohd-Yusof J (1997) For simulations of flow in complex geometries. Annual Research Briefs 317

  28. Bandringa H (2010) Immersed boundary methods. Master thesis, University of Groningen 9700

  29. Yang J, Stern F (2009) Sharp interface immersed-boundary/level-set method for wave-body interactions. J Comput Phys 228:6590–6616. https://doi.org/10.1016/j.jcp.2009.05.047

    Article  MathSciNet  MATH  Google Scholar 

  30. Calderer A, Kang S, Sotiropoulos F (2014) Level set immersed boundary method for coupled simulation of air/water interaction with complex floating structures. J Comput Phys 277:201–227. https://doi.org/10.1016/j.jcp.2014.08.010

    Article  MathSciNet  MATH  Google Scholar 

  31. Bihs H, Kamath A (2017) A combined level set/ghost cell immersed boundary representation for floating body simulations. Int J Num Methods Fluids 83:905–916. https://doi.org/10.1002/fld.4333

    Article  MathSciNet  Google Scholar 

  32. Zhao X, Ye Z, Fu Y, Cao F (2014) A cip-based numerical simulation of freak wave impact on a floating body. Ocean Eng 87:50–63. https://doi.org/10.1016/j.oceaneng.2014.05.009

    Article  Google Scholar 

  33. Yabe T, Xiao F, Utsumi T (2001) The constrained interpolation profile method for multiphase analysis. Journal of Computational physics 169:556–593. https://doi.org/10.1006/jcph.2000.6625

    Article  MathSciNet  MATH  Google Scholar 

  34. Xiao F, Ii S, Chen C (2011) Revisit to the thinc scheme: a simple algebraic vof algorithm. J Comput Phys 230:7086–7092. https://doi.org/10.1016/j.jcp.2011.06.012

    Article  MathSciNet  MATH  Google Scholar 

  35. Mittal R, Dong H, Bozkurttas M, Najjar F, Vargas A, Von Loebbecke A (2008) A versatile sharp interface immersed boundary method for incompressible flows with complex boundaries. J Comput Phys 227:4825–4852. https://doi.org/10.1016/j.jcp.2008.01.028

    Article  MathSciNet  MATH  Google Scholar 

  36. Hu C, Kashiwagi M (2009) Two-dimensional numerical simulation and experiment on strongly nonlinear wave-body interactions. J Mar Sci Technol 14:200–213. https://doi.org/10.1007/s00773-008-0031-4

    Article  Google Scholar 

  37. Pan D, Shen TT (2009) Computation of incompressible flows with immersed bodies by a simple ghost cell method. Int J Num Methods Fluids 60:1378–1401. https://doi.org/10.1002/fld.1942

    Article  MathSciNet  MATH  Google Scholar 

  38. Tseng YH, Ferziger JH (2003) A ghost-cell immersed boundary method for flow in complex geometry. J Comput Phys 192:593–623. https://doi.org/10.1016/j.jcp.2003.07.024

    Article  MathSciNet  MATH  Google Scholar 

  39. Franke R (1982) Scattered data interpolation: tests of some methods. Math Comput 38:181–200. https://doi.org/10.1090/S0025-5718-1982-0637296-4

    Article  MathSciNet  MATH  Google Scholar 

  40. Ross JM (2009) Human factors for naval marine vehicle design and operation. Ashgate Publishing, Ltd

  41. Ahmadzadeh M, Saranjam B, Fard AH, Binesh A (2014) Numerical simulation of sphere water entry problem using eulerian-lagrangian method. Appl Math Model 38:1673–1684. https://doi.org/10.1016/j.apm.2013.09.005

    Article  MathSciNet  MATH  Google Scholar 

  42. Lewis SG, Hudson DA, Turnock SR, Taunton DJ (2010) Impact of a free-falling wedge with water: synchronized visualization, pressure and acceleration measurements. Fluid Dyna Res 42:035509

    Article  Google Scholar 

  43. Tenzer M, Moctar Oe, Schellin TE (2015) Experimental investigation of impact loads during water entry. Ship Technol Res 62:47–59. https://doi.org/10.1179/0937725515Z.0000000003

    Article  Google Scholar 

  44. Panciroli R (2013) Water entry of flexible wedges: some issues on the fsi phenomena. Appl Ocean Res 39:72–74

    Article  Google Scholar 

  45. Sun H, Sun Z, Liang S, Zhao X (2019) Numerical study of air compressibility effects in breaking wave impacts using a cip-based model. Ocean Eng 174:159–168. https://doi.org/10.1016/j.oceaneng.2019.01.050

    Article  Google Scholar 

  46. Barjasteh M, Zeraatgar H, Javaherian MJ (2016) An experimental study on water entry of asymmetric wedges. Appl Ocean Res 58:292–304. https://doi.org/10.1016/j.apor.2016.04.013

    Article  Google Scholar 

  47. Yu P, Li H, Ong MC (2018) Numerical study on the water entry of curved wedges. Ships Offshore Struct 13:885–898. https://doi.org/10.1080/17445302.2018.1471776

    Article  Google Scholar 

  48. Camilleri J, Taunton D, Temarel P (2018) Full-scale measurements of slamming loads and responses on high-speed planing craft in waves. J Fluids Struct 81:201–229. https://doi.org/10.1016/j.jfluidstructs.2018.05.006

    Article  Google Scholar 

  49. Oger G, Doring M, Alessandrini B, Ferrant P (2006) Two-dimensional sph simulations of wedge water entries. J Comput Phys 213:803–822. https://doi.org/10.1016/j.jcp.2005.09.004

    Article  MathSciNet  MATH  Google Scholar 

  50. Lee J, Kim J, Choi H, Yang KS (2011) Sources of spurious force oscillations from an immersed boundary method for moving-body problems. J Comput Phys 230:2677–2695. https://doi.org/10.1016/j.jcp.2011.01.004

    Article  MathSciNet  MATH  Google Scholar 

  51. Masoomi M, Yousefifard M, Ramiar A (2017) Numerical investigation of symmetry and asymmetry rigid wedge slamming using openfoam code. Mod Mech Eng 17:343–352

    Google Scholar 

  52. Wen P, Qiu W, et al., (2016) Numerical prediction of forces and pressures onwedge and ship sections based on a cip method. In: The 26th International Ocean and Polar Engineering Conference, International Society of Offshore and Polar Engineers

  53. Xu L, Troesch A, Peterson R (1999) Asymmetric hydrodynamic impact and dynamic response of vessels. J Offshore Mech Arctic Eng 121:83–89

    Article  Google Scholar 

Download references

Acknowledgements

This study was partially supported by the National Natural Science Foundation of China (Grant No. 51679212), Zhejiang Provincial Natural Science Foundation of China (Grant No. LR16E090002), the Fundamental Research Funds for the Central Universities (Grant No. 2018QNA4041).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Xizeng Zhao.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zheng, K., Zhao, X., Yang, Z. et al. Numerical simulation of water entry of a wedge using a modified ghost-cell immersed boundary method. J Mar Sci Technol 25, 589–608 (2020). https://doi.org/10.1007/s00773-019-00666-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00773-019-00666-9

Keywords

Mathematics Subject Classification

Navigation