A Numerical Model of Vortex-Induced Vibration on Marine Risers

Authors

1 hormozgan university

2 Buein Zahra Technical University

Abstract

The Steger and Warming flux vector splitting implicit scheme is used to numerically solve two dimensional Reynolds Averaged Navier–Stokes (RANS) equations governing the vortex induced vibration of a flexible riser laterally supported by a spring and a damper. The k–ε model is used as turbulence model to simulate the turbulent flow in the wake of the riser. To update the new position of the riser, the lift coefficient obtained from the previous RANS iteration is coupled by the body motion equation. The proposed numerical solution is able to provide fair results in terms of lift coefficient, amplitude of oscillation and the effect of reduced velocity on it. The numerical results are compared with the available experimental and computational data where fairly good agreement even at the lock-in regime has been obtained. Taking wider external boundary, using conservative form of the equations, applying k-ε turbulence model for the separated flow and finally using the variable time step as the lock-in region approaches, are main features of the proposed numerical model.

Keywords


1- Griffin, O.M., and Ramberg, S.E., (1982), Some recent studies of vortex shedding with application to marine tubular sand risers. ASME Journal of Energy Resource Technology Vol.104, p.2–13.
2- Bearman, P.W., (1984), Vortex shedding from oscillating bluff bodies. Annual Review of Fluid Mechanics Vol.16, p.195–222.
3- Parkinson, G., (1989), Phenomena and modeling of flow-induced vibrations of bluff bodies. Progression Aerospace Sciences Vol.26, p.169–224.
4- Sarpkaya, T., (2004), A critical review of the intrinsic nature of vortex-induced vibrations, Journal of Fluids and Structures 1Vol.9, p.389–447.
5- Williamson, C.H.K., and Govardhan, R., (2004), Vortex-induced vibrations, Annual Review of Fluid Mechanics, Vol.36, p.413–455.
6- Bearman, P.W., (2000), Developments in Vortex Shedding Research, Workshop on Vortex-Induced Vibrations of Offshore Structures. Sao Paulo, Brazil.
7- Wanderley J.B., and Levi, C., (2005), Vortex induced loads on marine risers, Ocean Engineering Vol.32, p.1281–1295.
8- Khalak, A., and Williamson, C.H.K., (1996) Dynamics of a hydroelastic cylinder with very low mass and damping. Journal of Fluids and Structures, Vol.10, p.455–472.
9- Steger, J.L., and Warming, R.F, (1979), Flux vector splitting of invicid gas dynamic equations with application to finite difference method. NASA. TM-78605.
10- Favre, A., (1965) Equations des gaz turbulents compressibles: 1 Formes Ge´ne´rales. Journal of Mechanics, Vol.4, p.361–390.
11- Jones W.P., and Launder, B.E., (1997), The prediction of relaminarization with a two-equation model of turbulence, International Journal of Heat and Mass Transfer, Vol.15, p.301-314.
12- Goldberg, U.C., (1986), Separated flow treatment with a new turbulence model, AIAA Journal, Vol.24(10), p. 1711-1713.
13- Houzeaux, G., and Codina, R., (2003), A chimera method on a Dirichlet/Neumann (Robin) coupling for the Navier—Stokes equations. Computational Methods Application and Mechanical Engineering, Vol.192, p.3343–3377.
14- Herfjord, K., (1995), A study of two-dimensional separated flow by a combination of the finite element method and Navier–Stokes Equations, Dr. Eng. Theses, The Norwegian Institute of Technology, Trondheim, Norway.
15- Tritton, D.J., (1959), Experiments on the flow past a circular cylinder at low Reynolds number, Journal of Fluid Mechanics, Vol.6, p.