Current-induced vibration in multi-tube marine riser

This study looks at the non-linear behaviour of cylinder arrays subjected to fluid cross-flow. The emphasis is on the hysteresis phenomena, associated with fluidelastic excitation, which prove essential in the stability analysis in a low mass-damping parameter range typical for multi-tube marine risers. Since an array generates a high level of turbulence, this forcing mechanism is also included. The present work represents a significant departure from previous studies where attention was primarily focused on linearized fluid mechanics. -- A detailed experimental program, conducted in an attempt to reduce the number of degrees-of-freedom needed to model post-stable behaviour of a fully flexible cylinder array, provides a clear explanation for the underlying excitation mechanism. It shows that the fluid-damping force, associated with the transverse-to-flow motion of a single flexible cylinder, can induce hysteresis-type post-stable behaviour. That is, the underlying fluidelastic mechanism requires only one degree-of-freedom to operate. With this observation as a guide, a theoretical model is formulated. The proposed model is a modified time-domain version of an earlier linearized steady-state formulation for fluidelastic instability, developed by Lever and Weaver, which is based on one-dimensional flow and a phase lag between cylinder motion and flow adjustment. First, the fluidelastic equation of motion is solved analytically to third order using the first approximation method of Kryloff and Bogoliuboff. The effect of turbulence is examined via superposition of both excitation mechanisms (the random field of turbulence is represented by a flat power spectrum). Next, a fully non-linear solution is found using a direct numerical integration of the equation of motion. The essential features of the stability behaviour are discussed with the aid of bifurcation theory by analogy with corresponding static systems. -- The fluidelastic analysis predicts a stable limit cycle which becomes unstable as the mass-damping parameter is increased. Physical arguments, however, suggest that an opposite behaviour should occur, pointing to a weakness in the model formulated here. A significant improvement, leading also to prediction of hysteresis effects, is derived from an assumption that the phase lag is governed by cylinder motion and decreases with increasing oscillatory amplitude. The combined analysis shows that the fluidelastic stability boundary, when characterized by an unstable bifurcation, may be reduced by turbulence (the rate of reduction is directly proportional to turbulence strength and inversely proportional to unstable limit cycle). For a stable bifurcation, the fluidelastic stability boundary is virtually unaffected and the effect of turbulence is only apparent (interpretation of response curves)