Lock-in in the vortex-induced vibrations of a long tensioned riser in internal fluid flow and external uniform and shear flows: A prediction based on models

Abstract

In this study, the occurrence of lock-in, indicating local synchronization between the vortex shedding and cross-flow (CF) structural vibration frequencies, is investigated for a long tensioned and simply-supported riser conveying internal fluid flow that is free to move in the in-line (IL) and CF directions and immersed in uniform flow (UF) and linear shear flow (SF). Our established models are used to perform a numerical simulation, describing the unsteady hydrodynamic forces associated with wake dynamics using two van der Pol wake oscillators in the IL and CF directions coupled with the riser. The riser is discretized into a string of spatial slender beam elements, and the wake oscillators are distributed on the element nodes. MATLAB (R2014a) is used to establish a computational program verified using existing experimental data. The lock-in frequency and location are captured by comparing the wake model's CF oscillation frequency with the riser's CF vibration frequency at every node of the finite element system when both coincide at the frequency and location. The influences of the oncoming flow velocity, fluid's conveying velocity in the riser and the tension on the lock-in frequency, as well as the lock-in distribution along the riser axis, are discussed. In the UF, the high oncoming flow velocity (0.42 m s−1) promotes the occurrence of the lock-in at a higher frequency. When the oncoming flow velocity is high in the UF and linear SF, the internal fluid conveying velocity and tension have little influence on the lock-in condition. The present results do not always agree with the classic outcome in linear SF that the lock-in occurs in the region with a high oncoming flow velocity over at least 30% of the riser's length.