, Volume 53, Issue 10, pp 2585–2617 | Cite as

Hydroelastic analysis of water impact of flexible asymmetric wedge with an oblique speed

  • Mohammad Izadi
  • Parviz Ghadimi
  • Manouchehr Fadavi
  • Sasan Tavakoli


Current paper deals with hydroelastic impact of asymmetric and symmetric wedge sections with oblique speed into calm water. It is aimed to provide a better insight regarding fluid–structure interaction of the wedge sections of a high-speed craft into water in more realistic condition, in the presence of heel angle and oblique speeds. The defined problem is numerically investigated by coupled Finite Volume Method and Finite Element Method under two-way approach consideration. Accuracy of the proposed model is assessed in different steps. The results of current method are compared against previous experimental, numerical and theoretical methods and good agreement is displayed in these comparisons. Subsequently, the method is used in order to examine the fluid and structure behavior during the elastic impact of the wedge into water. Accordingly, four different physical situations are simulated. In the first part, symmetric impact with no oblique speed is simulated. The results of this part show fluctuations in vertical force and pressure of the midpoint during the impact time. Also, the relation of deadrise with deflection and pressure is observed in this part. In the second part, heel angle is also taken into consideration. It is concluded that the pressure and deflections at the right side of the wedge reduce, but these parameters increase at the left side. Moreover, it is observed that, the pressure at the midpoint of the left side of the wedge with deadrise angle of 10°, becomes negative, when the wall of the flexible wedge reaches its largest deflection. It is also observed that, the pressure at left side of the wedge with deadrise angle of 20°, reaches zero. Such behavior does not occur for the wedges of 30° and 45° deadrise angles. In the third part of simulations, oblique water entry of a flexible wedge of 20° deadrise angle is simulated, and no heel angle is considered. Harmonic behavior is observed for the vertical force, horizontal force, pressure of the midpoint and its deflection. First peaks of all of these variables are larger than the second peak. The obtained results lead us to conclude that an increase in oblique speed yields larger deflection and pressure at the right side. Meanwhile, no significant effect is observed for the left side of the wedge. Also, larger oblique speed is found to yield larger forces and angular moment. Final part of simulations involves the oblique water entry of a flexible wedge of 5° heel angle. Comparison of the results in the final part with that of third part, show that heel angle affects the pressure and deflection at both sides of the wedge. It is also observed that pressure and deflections of the left side increase, while those of right side increase. It is also seen that, similar as in the case of no heel angle, an increase in oblique speed leads to an increase of pressure and deflection at the starboard. It also leads to an increase in frequency of the vibration at right side.


Hydroelastic impact Fluid–structure interaction Asymmetric water entry Flexible body Oblique speed 


Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


  1. 1.
    Garme K, Rosén A, Stenius I, Kuttenkeuler J (2014) Rough water performance of lightweight high-speed craft. Proc Inst Mech Eng Part M J Eng Marit Environ 228(3):293–301Google Scholar
  2. 2.
    Barry C (2017) Rough water performance of lightweight high-speed craft. Mar Technol 54(2):18–21Google Scholar
  3. 3.
    Mu MA, Affendy S, Barki S, Adlina SF et al (2017) Mechanical behavior of potentially kapok hybrid composites in fibreglass boat. ARPN J Eng Appl Sci 12(1):3368–3372Google Scholar
  4. 4.
    Savitsky D (1985) Planing craft. Naval Eng J 97(2):113–141CrossRefGoogle Scholar
  5. 5.
    Faltinsen OM (2000) Hydroelastic slamming. J Mar Sci Technol 5(2):49–65CrossRefGoogle Scholar
  6. 6.
    Abrate S (2013) Hull slamming. Appl Mech Rev 64(6):060803ADSCrossRefGoogle Scholar
  7. 7.
    Faltinsen OM (2005) Hydrodynamics of high-speed marine vehicles. Cambridge University Press, CambridgeGoogle Scholar
  8. 8.
    Olausson K, Garme K (2015) Prediction and evaluation of working conditions on high-speed craft using suspension seat modelling. Proc Inst Mech Eng Part M J Eng Marit Environ 229(3):281–290Google Scholar
  9. 9.
    De Alwis MP, Lo Martire R, Äng BO, Garme K (2016) Development and validation of a web-based questionnaire for surveying the health and working conditions of high-performance marine craft populations. BMJ Open 6(6):e011681CrossRefGoogle Scholar
  10. 10.
    Martire RL, De Alwis MP, Äng BO, Garme K (2017) Construction of a web-based questionnaire for longitudinal investigation of work exposure, musculoskeletal pain and performance impairments in high-performance marine craft populations. BMJ Open 7(7):e016006CrossRefGoogle Scholar
  11. 11.
    De Alwis P, Garme K, Lo Martire R, Kasin JI, Ang B (2017) Crew acceleration exposure, health and performance in high-speed operations at sea. In: Proceedings of the 11th symposium on high-speed Marine Vehicles, Naples, ItalyGoogle Scholar
  12. 12.
    Savitsky D (2016) Direct measure of rigid body acceleration for water impact of a planing hull. J Ship Prod Des 32(2):1–10Google Scholar
  13. 13.
    Bowles J, Blount DL (2012) Turning characteristics and capabilities of high-speed monohulls. In: Proceedings of the third Chesapeake Powerboat Symposium, 2012, Annapolis, MDGoogle Scholar
  14. 14.
    Xu GD, Duan WY, Wu GX (2008) Numerical simulation of oblique water entry of an asymmetrical wedge. Ocean Eng 35:1597–1603CrossRefGoogle Scholar
  15. 15.
    Gu HB, Qian L, Causon DM, Mingham CG, Lin P (2014) Numerical simulation of water impact of solid bodies with vertical and oblique entries. Ocean Eng 75:128–137CrossRefGoogle Scholar
  16. 16.
    von Karman T (1929) The impact of seaplanes floats during landing. NACA TN 321Google Scholar
  17. 17.
    Wagner H (1932) Phenomena associated with impacts and sliding on liquid surfaces. NACA TranslationGoogle Scholar
  18. 18.
    Mackie AG (1969) The water entry problem. J Mech Appl Math 22(1):1–17ADSMathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Logvinovic GV (1969) Hydrodynamic of flows with free boundaries. Naukova Dumka, KievGoogle Scholar
  20. 20.
    Howison DS, Ockendon JR, Wilson SK (1991) Incompressible water-entry problems at small deadrise angles. J Fluid Mech 222:215–230ADSMathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    Kaplan P (1987) Analysis and prediction of flat bottom slamming impact of advanced marine vehicles in waves. Int Shipbuild Prog 34:44–53CrossRefGoogle Scholar
  22. 22.
    Cointe R, Armand JL (1987) Hydrodynamic impact analysis of a cylinder. J Offshore Mech Arct Eng 109:237–243CrossRefGoogle Scholar
  23. 23.
    Korobkin AA (2004) Analytical models of water impact. Eur J Appl Math 15:821–838MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    Korobkin AA, Melenica S (2005) Modified Logvinocich model for hydrodynamic loads on asymmetric contours entering water. In: Proceedings of the 20th international workshop on water waves and floating bodies, LongyearbyenGoogle Scholar
  25. 25.
    Korobkin AA (2007) Second-order Wagner theory of wave impact. J Eng Math 58(1–4):121–139MathSciNetCrossRefzbMATHGoogle Scholar
  26. 26.
    Tassin A, Piro DJ, Korobkin AA, Maki KJ, Cooker MJ (2013) Two-dimensional water entry and exit of a body whose shape varies in time. J Fluids Struct 40:317–336CrossRefGoogle Scholar
  27. 27.
    Qin H, Zhao L, Sing J (2011) A modified Logvinovich model for hydrodynamic loads on an asymmetric wedge entering water with a roll motion. J Mar Sci Appl 10:184–189CrossRefGoogle Scholar
  28. 28.
    Faltinsen OM, Kjaerland A, Nottveir A (1977) Water impact loads and dynamic response of horizontal circular cylinders in offshore structures. In: Proceedings of the 9th Annual Offshore Technology Conference, Huston, USGoogle Scholar
  29. 29.
    Xu L, Troesch AW, Vorous WS (1998) Asymmetric vessel impact and planing hydrodynamics. J Ship Res 42(3):187–198Google Scholar
  30. 30.
    Ghadimi P, Tavakoli S, Dashtimanesh A, Taghikhani P (2017) Dynamic Response of a wedge through asymmetric free fall in 2 degrees of freedom. Proc Inst Mech Eng Part M J Eng Marit Environ. Google Scholar
  31. 31.
    Weining F (1936) Berucksichtigung der elastizitat beim aufschlag eines gekielten flugzeugschwimmers auf das wasser (Ebenes Problem). Luftfahrtforschung 13:155–159Google Scholar
  32. 32.
    Povitsky AS (1935) Seaplane landing impact. Report no. 199, Central Aero-Hydrodynamical Institute, Moscow, pp 1–17Google Scholar
  33. 33.
    Povitsky AS (1939) The landing of seaplanes. Report no. 423, Central Aero-Hydrodynamical Institute, Moscow, pp 1–83Google Scholar
  34. 34.
    Meyerhoff WK (1965) Die berechnung hydroelastischer stosse. Schiffstechnik 12(60):18–30. (12(61), 49–64)Google Scholar
  35. 35.
    Vasin AD (1993) Hydroelastic interaction of a wedge-shaped construction entering a liquid. Fluid Dyn 28(3):387–392ADSCrossRefzbMATHGoogle Scholar
  36. 36.
    Faltinsen OM (1999) Water entry of a wedge by hydroelastic orthotropic plate theory. J Ship Res 43(3):180–193Google Scholar
  37. 37.
    Korobkin AA, Khabakhpasheva TI (2006) Regular wave impact onto an elastic plate. J Eng Math 55:127–150MathSciNetCrossRefzbMATHGoogle Scholar
  38. 38.
    Scolan YM (2004) Hydroelastic behaviour of a conical shell impacting on a quiescent-free surface of an incompressible liquid. J Sound Vib 277:163–203ADSCrossRefGoogle Scholar
  39. 39.
    Faltinsen OM (1997) The effect of hydroelasticity on ship slamming. Philos Trans Math Phys Eng Sci 355:575–591ADSCrossRefzbMATHGoogle Scholar
  40. 40.
    Faltinsen OM, Kvalsvold J, Aarsnes JV (1997) Wave impact on a horizontal elastic plate. J Mar Sci Technol 2:87–100CrossRefGoogle Scholar
  41. 41.
    Shams A, Porfiri M (2015) Treatment of hydroelastic impact of flexible wedges. J Fluids Struct 57:229–246CrossRefGoogle Scholar
  42. 42.
    Lu C, He Y, Wu G (2000) Coupled analysis of nonlinear interaction between fluid and structure during impact. J Fluids Struct 14:127–146CrossRefGoogle Scholar
  43. 43.
    Sun H (2007) A boundary element method applied to strongly nonlinear wave–body interaction problems. Ph.D. Thesis, Norwegian University of Science and Technology, Trondheim, NorwayGoogle Scholar
  44. 44.
    Bereznitsk A (2001) Slamming: the role of hydroelasticity. Int Shipbuild Prog 48(4):333–351Google Scholar
  45. 45.
    Stenius I, Rosen A, Kuttenkeuler J (2007) Explicit fe-modelling of hydroelasticity in panel-water impacts. Int Shipbuild Prog 54:111–127Google Scholar
  46. 46.
    Wall WA, Genkinger S, Ramm E (2007) A strong coupling partitioned approach for fluid–structure interaction with free surfaces. Comput Fluids 36:169–183CrossRefzbMATHGoogle Scholar
  47. 47.
    De Rosis A, Falcucci G, Porfiri M et al (2014) Hydroelastic analysis of hull slamming coupling lattice Boltzmann and finite element methods. Comput Struct 138(1):24–35CrossRefGoogle Scholar
  48. 48.
    Panciroli R, Abrate S, Minak G, Zucchelli A (2012) Hydroelasticity in water-entry problems: comparison between experimental and SPH results. Compos Struct 94:532–539CrossRefGoogle Scholar
  49. 49.
    Fourey G, Oger G, Le Touzé D, Alessandrini B (2010) Violent fluid–structure interaction simulations using a coupled SPH/FEM method. In: IOP conference series: materials science and engineering, p 012041Google Scholar
  50. 50.
    Yang X, Liu M, Peng S, Huang C (2016) Numerical modeling of dam-break flow impacting on flexible structures using an improved SPH–EBG method. Coast Eng 108:56–64CrossRefGoogle Scholar
  51. 51.
    Kihara H (2006) Numerical models of water impact. In: Proceedings of the 4th international conference on high-performance Marine Vehicles. Rome, ItalyGoogle Scholar
  52. 52.
    Ghadimi P, Feizi Chekab MA, Dashtimanesh A (2014) Numerical simulation of water entry of different arbitrary bow sections. J Naval Archit Mar Eng 11(2):117–129CrossRefGoogle Scholar
  53. 53.
    Ghadimi P, Feizi Chekab MA, Dashtimanesh A (2013) A numerical investigation of the water impact of an arbitrary bow section. ISH J Hydraul Eng 19(3):186–195CrossRefGoogle Scholar
  54. 54.
    Luo H, Wang S, Soares CG (2011) Numerical prediction of slamming loads on a rigid wedge subjected to water entry using an explicit finite element method, Advances in Marine Structures. Taylor & Francis, London, pp 41–47Google Scholar
  55. 55.
    Farsi M, Ghadimi P (2014) Finding the best combination of numerical schemes for 2D SPH simulation of wedge water entry for a wide range of deadrise angles. Int J Naval Archit Ocean Eng 6:638–651CrossRefGoogle Scholar
  56. 56.
    Farsi M, Ghadimi P (2016) Effect of flat deck on catamaran water entry through smoothed particle hydrodynamics. Proc Inst Mech Eng Part M J Eng Marit Environ 230(2):267–280CrossRefGoogle Scholar
  57. 57.
    Facci AL, Panciroli R, Ubertini S, Porfiri M (2015) Assessment of PIV-based analysis of water entry problems through synthetic numerical datasets. J Fluids Struct 55:484–500CrossRefGoogle Scholar
  58. 58.
    Facci AL, Porfiri M, Ubertini S (2016) Three dimensional water entry of solid body: a computational study. J Fluids Struct 66:36–53CrossRefGoogle Scholar
  59. 59.
    Shadmani R, Ghadimi P (2017) Parametric investigation of the effects of deadrise angle and demi-hull separation on impact forces and spray characteristics of catamaran water entry. J Braz Soc Mech Sci Eng 39(6):1989–1999CrossRefGoogle Scholar
  60. 60.
    Shademani R, Ghadimi P (2017) Numerical assessment of turbulence effects on forces, spray parameters, and secondary impact in wedge water entry problem using k-epsilon method. Sci Iran 24(1):223–236Google Scholar
  61. 61.
    Shadmani R, Ghadimi P (2017) Asymmetric water entry of twin wedges with different deadrises, heel angles, and wedge separations using finite element based finite volume method and VOF. J Appl Fluid Mech 10(1):353–368CrossRefGoogle Scholar
  62. 62.
    Feizi Chekab MA, Ghadimi P, Farsi M (2016) Investigation of three-dimensionality effects of aspect ratio on water impact of 3D objects using smoothed particle hydrodynamics method. J Braz Soc Mech Sci Eng 38(7):1987–1998CrossRefGoogle Scholar
  63. 63.
    Shadmani R, Ghadimi P (2017) Estimation of water entry forces, spray parameters and secondary impact of fixed width wedges at extreme angles using finite element based finite volume and volume of fluid methods. Brodogradnja 67(1):101–124Google Scholar
  64. 64.
    Farsi M, Ghadimi P (2015) Simulation of 2D symmetry and asymmetry wedge water entry by smoothed particle hydrodynamics method. J Braz Soc Mech Sci Eng 37(3):821–835CrossRefGoogle Scholar
  65. 65.
    Ghadimi P, Dashtimanesh A, Djeddi SR (2012) Study of water entry of circular cylinder by using analytical and numerical solutions. J Braz Soc Mech Sci Eng 34(3):225–232CrossRefGoogle Scholar
  66. 66.
    Javanmardi N, Ghadimi P, Tavakoli S (2018) Probing into the effects of cavitation on hydrodynamic characteristics of surface piercing propellers through numerical modeling of oblique water entry of a thin wedge. Brodogranja 69(2):151–158CrossRefGoogle Scholar
  67. 67.
    Izadi M, Ghadimi P, Fadavi M, Tavakoli S (2018) Numerical modeling of the freefall of two-dimensional wedge bodies into water surface. J Braz Soc Mech Sci Eng. Google Scholar
  68. 68.
    Reinhard M, Korobkin AA, Cooker MJ (2012) The bounce of a blunt body from a water surface at high horizontal speed. In: International workshop on water waves and floating bodies, Copenhagen, DenmarkGoogle Scholar
  69. 69.
    Faltinsen OM, Chazhain M (2005) A generalized Wagner method for three-dimensional slamming. J Ship Res 49(4):279–287Google Scholar
  70. 70.
    Korobkin AA, Scolan YM (2006) Three-dimensional theory of water impact. Part 2. Linearized Wagner problem. J Fluid Mech 549:413–427CrossRefGoogle Scholar
  71. 71.
    Ghadimi P, Saadatkhah A, Dashtimanesh A (2011) Analytical solution of wedge water entry by using schwartz–christoffel conformal mapping. Int J Model Simul Sci Comput 2(3):337–354CrossRefGoogle Scholar
  72. 72.
    Wang J, Laungi C, Faltinsen OM (2015) Experimental and numerical investigation of a freefall wedge vertically entering the water surface. Appl Ocean Res 51:181–203CrossRefGoogle Scholar
  73. 73.
    Wang J, Laungi C, Faltinsen OM (2015) Analysis of loads, motions and cavity dynamics during freefall wedges vertically entering the water surface. Appl Ocean Res 51:38–53CrossRefGoogle Scholar
  74. 74.
    Panciroli R, Porfiri M (2013) Evaluation of the pressure field on a rigid body entering a quiescent fluid through particle image velocimetry. Exp Fluids 54:1630–1642CrossRefGoogle Scholar
  75. 75.
    Jalalisendi M, Osma SJ, Porfiri M (2015) Three-dimensional water entry of a solid body: a particle image velocimetry study. J Fluids Struct 59:85–102CrossRefGoogle Scholar
  76. 76.
    Jalalisendi M, Shams A, Panciroli R, Porfiri M (2015) Experimental reconstruction of three-dimensional hydrodynamic loading in water entry problems through particle image velocimetry. Exp Fluids 56:1–17CrossRefGoogle Scholar
  77. 77.
    Panciroli R, Shams A, Porfiri M (2015) Experiments on the water entry of curved wedges: high speed imaging and particle image velocimetry. Ocean Eng 94:213–222CrossRefGoogle Scholar
  78. 78.
    Shams A, Jalalisendi M, Porfiri M (2015) Experiments on the water entry of asymmetric wedges using particle image velocimetry. Phys Fluids 27(2), Article No. 1Google Scholar
  79. 79.
    Ghadimi P, Tavakoli S, Dashtimanesh A (2017) Calm water performance of hard-chine vessels in semi-planing and planing regimes. Polish Marit Res 23(4):23–45Google Scholar
  80. 80.
    Ghadimi P, Tavakoli S, Dashtimanesh A, Zamanian R (2017) Steady performance prediction of heeled planing boat in calm water using asymmetric 2D + T model. Proc Inst Mech Eng M J Eng Marit Environ 231(1):234–257Google Scholar
  81. 81.
    Tavakoli S, Dashtimanesh A, Sahoo PK (2017) An oblique 2D + T approach for hydrodynamic modeling of yawed planing boats in calm water. J Ship Prod Des. Google Scholar
  82. 82.
    Tavakoli S, Dashtimanesh A (2017) Running attitudes of yawed planing hulls in calm water: development of an oblique 2D + T approach. J Ships Offshore Struct. Google Scholar
  83. 83.
    Morabito MG (2015) Prediction of planing hull side forces in yaw using slender body oblique impact theory. Ocean Eng 101:45–57CrossRefGoogle Scholar
  84. 84.
    Zarnickh EE (1978) A nonlinear mathematical model of motions of a planing boat in regular waves. David Taylor Naval Ship Research and Development Center, BethesdaGoogle Scholar
  85. 85.
    Zarnick EE (1978) A nonlinear mathematical model of motions of a planing boat in irregular waves. DTNSRDC. Report 79-0867-01. Bethesda, MD, USAGoogle Scholar
  86. 86.
    Akers RH (1999) Dynamic analysis of planing hulls in vertical plane. Paper Presented at: Proceedings of the Society of Naval Architects and Marine Engineers, New England SectionGoogle Scholar
  87. 87.
    van Deyzen A (2008) A nonlinear mathematical model for motions of a planing monohull In head seas. Paper Presented at: Proceedings of the 6th International Conference on High Performance Marine Vehicles, Naples, ItalyGoogle Scholar
  88. 88.
    Ghadimi P, Tavakoli S, Dashtimanesh A (2016) Coupled heave and pitch motions of planing hulls at non-zero heel angles. Appl Ocean Res 59:286–303CrossRefGoogle Scholar
  89. 89.
    Tavakoli S, Ghadimi P, Dashtimanesh A (2017) A non-linear mathematical model for coupled heave, pitch and roll motions of a high-speed planing hull. J Eng Math 104(1):157–194CrossRefzbMATHGoogle Scholar
  90. 90.
    Ghadimi P, Tavakoli S, Dashtimanesh A (2016) An analytical procedure for time domain simulation of roll motion of the warped planing hulls. Proc Inst Mech Eng M J Eng Marit Environ 230(4):600–615Google Scholar
  91. 91.
    Zhao R, Faltinsen OM (1993) Water entry of two-dimensional bodies. J Fluid Mech 246:593–612ADSCrossRefzbMATHGoogle Scholar
  92. 92.
    Tveitnes T, Flailie-Clarke AC, Varyani K (2008) An experimental investigation into the constant velocity water entry of wedge-shaped sections. Ocean Eng 35:1463–1478CrossRefGoogle Scholar
  93. 93.
    Xu L (1998) A theory for asymmetrical vessel impact and steady planing. Ph.D. Thesis, University of Michigan, Ann Arbor, Michigan, USGoogle Scholar
  94. 94.
    Toyoma Y (1993) Two-dimensional water impact of unsymmetrical bodies. J Soc Naval Archit Jpn 173:285–291CrossRefGoogle Scholar

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Authors and Affiliations

  1. 1.Department of Marine TechnologyAmirkabir University of TechnologyTehranIran

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