Vortex-induced vibrations of pipes conveying pulsating fluid

• Vortex-induced vibrations of a pipe conveying fluctuating flows are analyzed.
• Effect of internal pulsating fluid flow on the dynamics is found to be pronounced.
• The system displays both multi-value and single-value responses.
• Hysteresis may occur with small increment or decrement of the detuning parameter.

The vortex-induced vibrations of a long flexible pipe conveying fluctuating flows are investigated via a two-mode discretization of the governing differential equations. In the present work, the internal fluid velocity is assumed to have a harmonically varying component superposed on a steady mean velocity. Direct perturbation method of multiple scales (MMS) is adopted to transform the governing nonlinear partial differential equations (PDEs) into ordinary differential equations (ODEs), which are then analyzed numerically for the pipe with principal parametric resonances during lock-in for each of the first two modes. The results indicate that in the case of a pipe containing fluctuating flows, the peak of vibration amplitudes is larger than that of a pipe conveying steady flows. With the increase of detuning parameter for the frequency of pulsating flow, the variation range of vibration amplitudes of the pipe enlarges first and then narrows, with jumping phenomenon that the vibration amplitude changes from multi-value to single-value and then returns to multi-value between the two regions of multi-value responses, which has not been discovered yet. From the amplitude-frequency response curves one can see that the hysteresis may occur with small increments or decrements of the detuning parameter. It is also found that if the pipe system is in the lock-in condition for a certain mode, the pulsating component can have an obvious impact on the dynamics of the pipe only when the parametric resonance occurs in the same mode. In addition, the method of numerical simulations (MNS) is directly employed to verify our implementation of MMS.