This study is aimed at understanding the hydrodynamic phenomena of 8-shaped oscillating flexible risers for upwelling deep ocean water. The 8-shaped oscillations of flexible risers are observed when the Keulegan-Carpenter numbers are higher than 7, and these oscillations are actually 8-shaped figures constantly repeated at the bottom end of the hanging-off flexible riser. The authors have developed a dynamic analysis method of flexible risers for upwelling deep ocean water. The analysis method can predict in-line dynamics of oscillating risers at low Kc numbers. In this analysis, a symmetrical vortices model has been used to estimate in-line hydrodynamic forces on the riser elements. The purpose of this paper is to apply the above approach to the 8-shaped oscillating flexible risers. Motion measurements of forced oscillating pipe models are carried out with changing the structural parameters, to investigate the conditions when the 8-shaped oscillations occur.
Many researches on floating-type facilities including ocean thermal energy conversion (OTEC) plants for upwelling deep ocean water have been carried out (e.g., Avery and Wu, 1994). For the floating-type facilities, flexible risers are often used as the deep ocean water upwelling pipe, but the accurate dynamic analysis of flexible pipe is one of the most important technical subjects. Many researchers have developed Dynamic analysis methods of flexible risers (e.g. Chakrabarti and Frampton, 1982). In these methods, Morison equation is generally used for estimating the external viscous hydrodynamic forces. In Morison equation, the hydrodynamic coefficients (drag and added-mass coefficients, Cd and Ca) depend on Keulegan-Carpenter number (Kc) and Reynolds number (Re). Because considerations of Kc and Re variations with the pipe motion itself are required, an iterative calculation technique would be applicable to only steady solutions in regular oscillation conditions (e.g. Suzuki and Yoshida, 1990).