Analyses of fluid-solid coupling dynamics of elastic tubes vibrating in cross flows

Treatments on dynamic interfaces and fluid-solid coupling are critical in systems of tubes vibrating in fluids that are common in tube-strings of deep-water oil drilling systems, marine cluster wells and heat exchangers. This paper proposes a “weakly” coupled algorithm for modeling vortex induced vibrations of elastic tubes submerged in cross flows. In the present algorithm, the elastic tube is discretized with beam elements and the fluid is discretized with volume elements, and the grids for both the tube and fluid is perfectly marched on the interface. Using the shape functions of beam elements, the formula for displacement, velocity, and force approximations are carried out, and convergence criterion analyses are also performed for the fluid-solid coupling interfaces. The present weakly coupling algorithm is developed with a sub-iteration loop to ensure accuracy in handling the dynamic coupling between the elastic tube and fluid. The vortex-induced vibrating characteristics are then analyzed for various elastic tubes at different natural frequencies. Intensive numerical studies are also conducted to examine the effects of the ratio of the elastic tube's natural frequency to the static flow's frequency. It is found that the change of frequency ratio has less effect on the fluid pressure and velocity distributions on the surface of the elastic tube, but more effects on the vibration of the tube. When the frequency ratio is less than 1.009, the vibrating amplitude, period and trajectory of elastic tube decrease with the increase of frequency ratio. While if the frequency ratio is more than 1.009, the vibrating amplitude, period and trajectory are almost unchanged and the elastic tube behaves similarly to a rigid tube. It is also found that there is a critical frequency ratio for a vortex-induced vibration to occur for tubes in cross flows. This finding is important for the prevention of violent vibrations of tubular structures in flows, such as deep-water oil drilling tube-strings, marine cluster wells and heat exchangers.