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

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.

Keywords

phase flow / Stokes wave / ship hull / numerical tank / free surface wave / artifical beach / volume of fluid (VOF) / finite volume method (FVM)

References

[1] Ashgriz N, Barbat T, Wang G. A computational Lagrangian-Eulerian advection remap for free surface flows. International Journal for Numerical Methods in Fluids, 2004, 44(1): 27-32

[2] Bai W, Eatock T R. Fully nonlinear simulation of wave interaction with fixed and floating flares structures. Ocean Engineering, 2009, 36: 223-236

[3] Cao H. The computation and research on resistance of planning craft based on the software FLUENT. M.Eng thesis, Harbin Engineering University, 2008

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

[5] Chen HC, Lee SK. Interactive RANS/Laplace method for nonlinear free surface flows. Journal of Engineering Mechanics, 1996, 122(2): 153-162

[6] Christensen ED. Large eddy simulation of spilling and plunging breakers. Coastal Eng., 2006, 53: 464-485

[7] Constantin A, Strauss W. Exact steady periodic water waves with vorticity. Comm. Pure Appl. Math., 2004, 57: 481-527

[8] Constantin A, Sattinger D, Strauss W. Variational formulations for steady water waves with vorticity. J. Fluid Mech., 2006, 548: 151-163

[9] Constantin A, Strauss W. Stability properties of steady water waves with vorticity. Comm. Pure Appl. Math., 2007, 60: 911-950

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

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

[12] Guignard S, Grilli ST, Marcer R, Rey V. Computation of shoaling and breaking waves in near shore areas by the coupling of BEM and VOF methods. Computers & fluids, 1999, 5: 304-309

[13] Hackensack NJ, Christensen ED, Deigaard R. Large eddy simulation of breaking waves. Coastal Eng., 2001, 42: 53-86

[14] Henry D. The trajectories of particles in deep-water Stokes waves. Int. Math. Res. Not. Art., 2006, 13: 23405-23410

[15] Henry D. On the deep-water Stokes wave flow. Int. Math. Res. Not. Art., 2008, 7: 71-79

[16] Kouh JS, Lin TJ, Chau SW. Performance analysis of two-dimensional hydrofoil under free surface. J. Natl. Taiwan Univ., 2002, 86: 113-122

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

[18] Lara JL, Losada IJ, Liu P-F. Breaking waves over a mild gravel slope: experimental and numerical analysis. Journal of Geophysical Research, 2006, 111: 1-26

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

[20] Sitanggang KI, Lynett PJ, Liu PLF. Development of a Boussinesq-RANS VOF hybrid wave model. Proceedings of the International Conference Coastal Engineering, 2006, 1: 24-35

[21] Stokes. On the theory of the oscillatory waves. Trans. Camb. Phil. Soc., 1847, 8: 441-445

[22] Teng B, Kato S. Third order wave force on axisymmetric bodies. Ocean Engineering, 2002, 29: 815-843

[23] Wang Z, Niu J, Qin Z, Pang Y. Numerical simulation calculation for planing vessel resistancebased on FLUENT. The 14th China Ocean (Coast) Engineering Symposium Proceedings, Huhehaote, China, 2009, 309-315

[24] Zhang XS, Beck RF. Three-dimensional large-amplitude body motions in waves. Journal of Offshore Mathematics and Arctic Engineering, 2008, 130(4): 509-518