Skip to main content
Log in

Numerical simulation of the stokes wave for the flow around a ship hull coupled with the VOF model

  • Published:
Journal of Marine Science and Application Aims and scope Submit manuscript

Abstract

The surface wave generated by flow around a ship hull moving near free surface of water is simulated numerically in this study. The three-dimensional implicit finite volume method (FVM) is applied to solve Reynolds averaged Navier-Stokes (RANS) equation. The realizable k-e turbulence model has been implemented to capture turbulent flow around the ship hull in the free surface zone. The volume of fluid (VOF) method coupled with the Stokes wave theory has been used to determine the free surface effect of water. By using is a six degrees of freedom model, the ship hull’s movement is numerically solved with the Stokes wave together. Under the action of Stokes waves on the sea, the interface between the air and water waves at the same regular pattern and so does the pressure and the vertical velocity. The ship hull moves in the same way as the wave. The amplitude of the ship hull’s heave is less than the wave height because of the viscosity damping. This method could provide an important reference for the study of ships’ movement, wave and hydrodynamics.

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.

Similar content being viewed by others

References

  • Ashgriz N, Barbat T, Wang G(2004). A computational Lagrangian-Eulerian advection remap for free surface flows. International Journal for Numerical Methods in Fluids, 44(1), 27–32. DOI: 10.1002/fld.620

    Article  MathSciNet  Google Scholar 

  • Bai W, Eatock Taylor R (2009). Fully nonlinear simulation of wave interaction with fixed and floating flares structures. Ocean Engineering, 36, 223–236.

    Article  Google Scholar 

  • Cao Hongjian (2008). The computation and research on resistance of planning craft based on the software FLUENT. M.Eng thesis, Harbin Engineering University.

    Google Scholar 

  • Chen CK, Liu H (2005). A submerged vortex lattice method for calculation of the flow around three-dimensional hydrofoil. J. Ship Mech., 9(2), 41–45

    Google Scholar 

  • Chen HC, Lee SK (1996). Interactive RANS/Laplace method for nonlinear free surface flows. Journal of Engineering Mechanics. 122(2), 153–162.

    Article  Google Scholar 

  • Christensen ED (2006). Large eddy simulation of spilling and plunging breakers. Coastal Eng., 53, 464–485. DOI: 10.1016/j.coastaleng.2005.11.001

    Article  Google Scholar 

  • Constantin A, Strauss W (2004). Exact steady periodic water waves with vorticity. Comm. Pure Appl. Math., 57, 481–527.

    Article  MATH  MathSciNet  Google Scholar 

  • Constantin A, Sattinger D, Strauss W (2006). Variational formulations for steady water waves with vorticity. J. Fluid Mech., 548, 151–163.

    Article  MathSciNet  Google Scholar 

  • Constantin A, Strauss W (2007). Stability properties of steady water waves with vorticity. Comm. Pure Appl. Math., 60, 911–950. DOI: 10.1002/cpa.20165

    Article  MATH  MathSciNet  Google Scholar 

  • Dong CM, Huang CJ (2004). Generation and propagation of water waves in a two-dimensional numerical viscous wave flume. Journal of Waterway Port, Coastal and Ocean Engineering, 130(3), 143–153.

    Article  Google Scholar 

  • Grilli ST, Gilbert R, Lubin P, Vincent S, Astruc D, Duval M, Kimmoun O, Branger H, Devrard D, Fraunié P, Abadie S (2004). Numerical modeling and experiments for solitary wave shoaling and breaking over a sloping beach. The International Society of Offshore and Polar Engineers, Toulon, France 306–312.

    Google Scholar 

  • Guignard S, Grilli ST, Marcer R, Rey V (1999). Computation of shoaling and breaking waves in near shore areas by the coupling of BEM and VOF methods. Computers & fluids 5, 304–309.

    Google Scholar 

  • Hackensack NJ, Christensen ED, Deigaard R (2001). Large eddy simulation of breaking waves. Coastal Eng., 42, 53–86. DOI: 10.1016/S0378-3839(00)00049-1

    Article  Google Scholar 

  • Henry D (2006). The trajectories of particles in deep-water Stokes waves. Int. Math. Res. Not. Art., 13, 23405–23410. DOI: 10.1016/j.wavemoti.2009.06.007

    MathSciNet  Google Scholar 

  • Henry D (2008). On the deep-water Stokes wave flow. Int. Math. Res. Not. Art., 7, 71–79.

    Google Scholar 

  • Kouh JS, Lin TJ, Chau SW (2002). Performance analysis of two-dimensional hydrofoil under free surface. J. Natl. Taiwan Univ., 86, 113–122

    Google Scholar 

  • Li JB, Zhang NC, Guo CS (2010). numerical simulation of waves interaction with a submerged horizontal twin-plate breakwater. China Ocean Engineering, 24(4), 627–640.

    Article  MathSciNet  Google Scholar 

  • Lara JL, Losada IJ, Liu PL-F (2006). Breaking waves over a mild gravel slope: experimental and numerical analysis. Journal of Geophysical Research, 111, C11019, 1–26.

    Google Scholar 

  • Li TQ, Troch P, de Rouck J, Goossens D (2005). Numerical simulation of water wave impacts using a Navier-Stokes solve. Proceedings of the 29th International Conference on Coastal Engineering, 4100–4112.

    Google Scholar 

  • Sitanggang KI, Lynett PJ, Liu PLF (2006). Development of a Boussinesq-RANS VOF hybrid wave model. Proceedings of the International Conference Coastal Engineering, San Diego, California, USA, 1, 24–35. DOI: 10.1142/9789812709554_0003

    Google Scholar 

  • Stokes (1847). On the theory of the oscillatory waves. Trans. Camb. Phil. Soc., 8, 441–445.

    Google Scholar 

  • Teng B, Kato S (2002). Third order wave force on axisymmetric bodies. Ocean Engineering, 29, 815–843. DOI: 10.1016/S0029-8018(01)00047-6

    Article  Google Scholar 

  • Wang Zhaoli, Niu Jianglong, Qin Zaibai, Pang Yongjie (2009). Numerical simulation calculation for planing vessel resistancebased on FLUENT. The 14th China Ocean (Coast) Engineering Symposium Proceedings, Huhehaote, China, 309–315.

    Google Scholar 

  • Zhang XS, Beck RF (2008). Three-dimensional large-amplitude body motions in waves. Journal of Offshore Mathematics and Arctic Engineering, 130(4), 509–518. DOI: 10.1016/j.oceaneng.2008.11.003

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Zhong Jingjun.

Additional information

Foundation item: Supported by National Natural Science Foundation of China (51409031), Fundamental Research Funds for the Central Universities (3132015203) and China Postdoctoral Science Foundation (2014M561216).

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Shengtao, C., Jingjun, Z. & Peng, S. Numerical simulation of the stokes wave for the flow around a ship hull coupled with the VOF model. J. Marine. Sci. Appl. 14, 163–169 (2015). https://doi.org/10.1007/s11804-015-1305-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11804-015-1305-y

Keywords

Navigation