Numerical Simulations of the Flow Around Flexible Cylinders

In the offshore industry fluids are conveyed from the seabed to the platform through slender structures named risers. These risers are subject to shear and oscillatory flows due to currents and waves respectively, flows with a very high degree of complexity, with changes of intensity and direction the deeper the water depth. The main purpose of this work is to investigate the hydroelastic interactions which take place between flexible cylinders and fluid forces. The cylinders are subject to uniform flow, and the hydrodynamic forces are estimated by CFD, in a quasi three-dimensional fashion. This article presents the results of an investigation being carried out at the University of Sa˜o Paulo and sponsored by the Brazilian Oil Company Petrobras. In this research a discrete vortex method is used to simulate the flow around a flexible cylinder. A description of this method can be found at Yamamoto et al. (OMAE 2001). A finite element structural model based on the Euler-Bernoulli beam theory was developed. In order to evaluate the dynamic response, a general equation of motion is solved through a numerical integration scheme in the time domain. The hydrodynamic forces are evaluated in two-dimensional strips. The technique used is the Discrete Vortex Method, which is a Lagrangian numerical scheme to simulate an incompressible and viscous fluid flow. The calculations are compared with experiments of a cantilever flexible cylinder immersed in a current, see Fujarra [6]. The reduced velocity vs. non-dimensional amplitude curve obtained in our calculations is compared with the experimental results. Visualizations of the wake indicate a hybrid mode of vortex shedding along the span. A 2S mode is found in regions of low amplitudes, changing to a 2P mode in the regions o larger amplitudes. The position of the transition of the modes varies with the reduced velocity. A practical case of marine risers is also presented. In this case the results for various uniform currents acting on a single, flexible cylinder, representing a riser of 120m with 100m under water, are shown. Envelopes of maximum and minimum in-line and transverse displacements are presented.