Otc 11998

Vortex-induced vibration (VIV) of a long riser in sheared current is often considered as an energy balance problem: Excitation forces in the power-in region add an equal amount of energy to the system as is dissipated by damping forces outside this region and structural damping. A riser may have different excitation and damping regions depending on the actual oscillation frequency, cross-section properties and local flow velocity. A damping model must hence be able to handle higher and lower flow velocities than the excitation velocity range. In this paper the fluid damping models proposed by Venugopal [1] are compared with the experiments conducted by Gopalkrishnan [2] and Vikestad [3]. The results show that the models are conservative at high and low reduced velocities. Introduction VIV is dependent on many factors such as the Reynolds number, flow velocity and turbulence of the incident current, surface roughness, cross-section shape, inclination, motion of the structure, etc. No solutions or models exist which can account for all these factors. The solution has therefore been to simplify the interaction problem as much as possible hopefully without loosing the information important for the prediction of the resulting VIV and fatigue life of the riser. One such simplification is to assume that each cross-section along the riser is oscillating harmonically in the cross-flow direction only and that the incident flow is constant in time. Then the fluid forces can be split into two parts; the inertia part in phase with the acceleration and the excitation/damping part in phase with the velocity of the cross-section. If the force in phase with velocity has the same sign as the velocity it is excitation, if it has opposite sign it is damping. In this paper we compare the damping model presented by Venugopal [1] to other experiments. The model predicts the damping force for oscillations in still water, at velocities lower than the excitation velocity range, and at higher. The Venugopal model was based on published empirical damping data from sub-critical flow experiments. In this paper the Venugopal model is further tested against the experimental data gathered by Vikestad [3]. The model was found to be slightly conservative in that it tends to underestimate the damping, but not overly so. The special feature of Vikestad’s experiments is that they reveal the damping on a freely vibrating spring-mounted cylinder. The damping is evaluated at a frequency which is different than the local vortex shedding frequency. This emulates the situation when two frequencies are competing on a long riser subjected to sheared current. Response from one excitation region is damped out in the excitation region of the other frequency. Damping of VIV Dynamic equilibrium The dynamic equilibrium equation for a single degree of freedom system with mass m, structural damping cstr, stiffness k, and an excitation force Fv is given as: v str F kx x c x m .......................................................(1) If Fv is a single harmonic force, Fv = F0 sin( t+ ), and is the phase between the force and the motion, x = x0 sin( t), Eq. (1) can be written as 0 kx x ) c c ( x ) am m ( f str ..................................(2) where am is the added mass: