Journal of Hydrodynamics

, Volume 18, Issue 1, pp 137–143

# A finite element solution of wave forces on a horizontal circular cylinder close to the sea-bed

• Ming Zhao
• Liang Cheng
• Hongwei Ah
Session B2

## Abstract

A numerical model is established for simulating the wave action on a horizontal circular cylinder close to the sea-bed. The two-dimensional Navier-Stokes (NS) equations are solved by a finite element method. The arbitrary Lagrangian-Eulerian scheme is employed for tracking the moving free surface boundary. After each computational time step, the mesh is updated by solving a linear equilibrium equation of elasticity. In front of the outgoing boundary a damping layer is set to absorb the wave energy. The computation is carried out for the gap between the cylinder and sea bed (e) ranging from 0.1 to 1.5D, with D being the cylinder diameter, and the Reynolds number about 1800. The computed wave force coefficients and velocity fields are verified by the experimental results reported by Jarno-Druaux et al. (1995).

## Key words

wave circular cylinder finite element method navier-stokes equations hydrodynamic forces

## References

1. [1]
Otsuka, K., Ikeda, Y. Estimation of inertia forces on a horizontal circular cylinder in regular and irregular waves at low Keulegan-Carpenter numbers [J]. Applied Ocean Research, 1996, 18: 145–156.
2. [2]
Chaplin, J. R., Subbiah, K. Large scale horizontal cylinder forces in waves and currents [J]. Applied Ocean Research, 1997, 19: 211–223.
3. [3]
Contento, G., Codiglia, R. Non-linear free surface induced pressure on a submerged horizontal circular cylinder at low Keulegan-Carpenters number [J]. Applied Ocean Research, 2001, 23: 175–185.
4. [4]
Sarpkaya, T. In line and transverse forces on oscillatory flow at high Reynolds numbers [J]. Journal of Ship Research, 1977, 21(4): 200–216.Google Scholar
5. [5]
Sarpkaya, T., Rajabi, F. Hydrodynamic drag on bottom mounted smooth and rough cylinders in periodic flow [A]. 11th Annual Offshore Technology Conference, Houston, TX, 1979: 219–226.Google Scholar
6. [6]
Sumer, B. M., Jensen, B. L., Fredsøe, J. Effect of a plane boundary on oscillatory flow around a circular cylinder [J]. Journal of Fluid Mechanics, 1991, 225: 271–300.
7. [7]
Justesen, P., Hansen, E.A., Fredsøe, J., Bryndum, M.B., Jacobsen, V. Forces on and flow around near-bed pipelines in waves and current [A]. Proceedings of the Sixth International Offshore Mechanics and Arctic Engineering Symposium, ASME, Houston, TX, 1987, 2: 131–138.Google Scholar
8. [8]
Jarno-Druaux, A., Sakout, A., Lambert, E. Interference between a circular cylinder and a plane wall under waves [J]. Journal of Fluids and Structures, 1995, 9: 215–230.
9. [9]
Cokgor, S. Hydrodynamic forces on a partly buried cylinder exposed to combined waves and current [J]. Ocean Engineering, 2002, 29: 753–768.
10. [10]
Armenio, V. Dynamic loads on submerged bodied in a viscous numerical wave tank at small KC number [J]. Ocean Engineering, 1998, 25 (10): 881–905.
11. [11]
Zhu, G., Borthwick, A. G. L., Eatock Talor, R. A finite element model of interaction between viscous surface waves and submerged cylinders [J]. Ocean Engineering, 2001, 28: 989–1008.
12. [12]
Soulaimani, A., Saad, Y. An arbitrary Lagrangian-Eulerian finite element method for solving three-dimensional free surface flows [J]. Computer Methods in Applied Mechanics and Engineering, 1998, 162 (1–4): 79–106.
13. [13]
Braess, H., Wriggers, P. Arbitrary Lagrangian Eulerian finite element analysis of the free surface flow [J]. Comput. Methods Appl. Mech. Engrg., 2000, 190: 95–109.
14. [14]
Lo, D. C., Young, D. L. Arbitrary Lagrangian-Eulerian finite element analysis of free surface flow using a velocity-vorticy formulation [J]. Journal of Computational Physics, 2004, 195: 175–201.
15. [15]
Johnson, A. A., Tezduyar, T. E. Mesh update strategies in parallel finite element computations of flow problems with moving boundaries and interfaces [J]. Comput. Methods Appl. Mech. Engrg., 1994, 119: 73–94.
16. [16]
Hughes, T. J. R., Liu, W. K., Zimmerman, T. K. Lagrangian Eulerian finite element formulation for incompressible viscous flows [J]. Comput. Meth. Appl. Mech. Engrg., 1981, 29: 329–349.
17. [17]
Apsley, D., Hu, W. CFD simulation of two- and three-dimensional free-surface flow [J]. International Journal for Numerical Methods in Fluids, 2003, 42: 465–491.
18. [18]
Larsen, J., Dancy, H. Open boundaries in short wave simulation—a new approach [J]. Coastal Eng., 1983, 7 (3): 285–297.
19. [19]
Zhao, M., Cheng, L., Teng, B., Dong, G., Hydrodynamic forces on dual cylinders of different diameters in steady currents [J]. Submitted to Journal of Fluids and Structures, 2005.Google Scholar