A numerical simulation model for the vortex induced vibration of flexible risers using dynamic stiffness matrices

In this study, a time-domain numerical method using dynamic stiffness matrices is proposed to obtain the characteristics of the vortex induced vibration (VIV) of a flexible riser. Due to the large ratio of length to diameter, a marine riser is approximated as a cable model. Based on the finite volume method (FVM), the cable model of the riseris dividedinto a certain number of segments. The dynamic stiffness matrix of each segment reflecting the time varying strain energy and bending stiffness are updated in calculation. The total dynamic stiffness matrix of the riser is then obtained by the superposition characteristics of the finite volume method. In the nonlinear governing equation of riser's vibration, the hydrodynamic forces are calculated by the instantaneous vorticity conserved boundary condition (IVCBC) method and the equation is solved by the step-by-step time integration method to obtain the accelerations, velocities and displacements of the riser. Validation of this numerical approach is carried out by comparing the static balance and the dynamic responses with quantities in classical experimental cases for a riser in uniform flow. The results show that:when the vibration of riser is high order mode vibration, the dynamic stiffness matrix cannot be ignored. The vortex induced vibration of the given flexible riser has a strong coupling effect between the deformation of riser and flow field. In the vibtation of the riser, there exists the multiple-frequency effect, numely, adominant frequency co-exists with some subordinate frequencies, hence the shedding frequencies can no longer be satisfied with the distributions of the Strauhal number. The wake effect onthe vortex shedding has a stronger 3-dimensional effect at the locations of smaller lateral vibrations. The numerical simulations also reveal that the vibration mode increases with the flow velocity.