Coupled cross-flow and in-line vortex-induced vibrations of a cantilevered pipe with a concentrated mass end

In this paper, a numerical study based on a wake oscillator model has been conducted to determine the vortex-induced vibration (VIV) response performances of the coupled cross-flow (CF) and in-line (IL) vibrations of a cantilevered flexible pipe with a concentrated mass at the free end. First, the coupled equations for both the CF and IL vibrations of the structure are established based on the vector analysis theory. Subsequently, the governing equations of the structural vibration and flow excitation have been numerically solved using the finite difference method. Finally, the VIV response characteristics including the vibration displacement, vibration frequency, vibration trajectory, and energy transfer under different current velocities have been systematically investigated. The numerical results show that the behavior of both the standing wave and travelling wave dominate the VIV displacement in CF and IL directions. The travelling wave behavior in the IL direction is more pronounced compared with that in the CF direction. As the current velocity increases, the traveling wave propagation speeds in both the CF and IL directions exhibit a decreasing trend. The vibration frequency in the CF direction is characterized by a single dominant frequency with a narrow-band distribution, whereas in the IL direction, it shows multi-frequency characteristics with a broadband distribution. The vibration displacement at the pipe end is disordered, which is caused by variations in the mean vibration displacement in both the CF and IL directions. The energy input region from the fluid to the structure is mainly concentrated near the pipe end. The energy transferred from the fluid to the structure is much smaller in the IL direction than in the CF direction.