Flow-induced vibrations of a deformable ring

To understand flow-induced vibrations of deformable objects, we numerically investigate dynamics of a pressurized elastic ring pinned at one point within a uniform flow by using an immersed-boundary algorithm. The boundary of the ring consists of a fibre with no bending stiffness, which can be modelled as a linear spring with spring constant k and zero unstretched length. The vibration of the ring is decomposed into two parts: a pitching motion that includes a rigid-body rotation and a flexible bending motion in the transverse direction, and a tapping motion in the longitudinal direction. The pitching motion is dominated by the frequency of vortex shedding, whereas the primary frequency of the tapping motion is twice the frequency of vortex shedding. At the Reynolds number of 100, resonance is observed when k similar to 0.2 (k is normalized by the diameter of the undeformed ring, the speed of the upcoming flow and the fluid density). Across the resonance region, abrupt jumps in terms of the motion amplitudes as well as the hydrodynamic loads are recorded. Within the resonance region, the lift force demonstrates a beating phenomenon reminiscent of findings through reduced models and low-degree-of-freedom systems.