The onset of vortex-induced vibrations of a flexible cylinder at large inclination angle

Abstract

The onset of the vortex-induced vibration (VIV) regime of a flexible cylinder inclined at$80^{\circ }$within a uniform current is studied by means of direct numerical simulations, at Reynolds number$500$based on the body diameter and inflow velocity magnitude. A range of values of the reduced velocity, defined as the inverse of the fundamental natural frequency, is examined in order to capture the emergence of the body responses and explore the concomitant reorganization of the flow and fluid forcing. Additional simulations at normal incidence confirm that the independence principle, which states that the system behaviour is determined by the normal inflow component, does not apply at such large inclination angle. Contrary to the normal incidence case, the free vibrations of the inclined cylinder arise far from the Strouhal frequency, i.e. the vortex shedding frequency downstream of a fixed rigid cylinder. The trace of the stationary body wake is found to persist beyond the vibration onset: the flow may still exhibit an oblique component that relates to the slanted vortex shedding pattern observed in the absence of vibration. This flow component which occurs close to the Strouhal frequency, at a high and incommensurable frequency compared to the vibration frequency, is referred to as Strouhal component; it induces a high-frequency component in fluid forcing. The vibration onset is accompanied by the appearance of novel, low-frequency components of the flow and fluid forcing which are synchronized with body motion. This second dominant flow component, referred to as lock-in component, is characterized by a parallel spatial pattern. The Strouhal and lock-in components of the flow coexist over a range of reduced velocities, with variable contributions, which results in a variety of mixed wake patterns. The transition from oblique to parallel vortex shedding that occurs during the amplification of the structural responses, is driven by the opposite trends of these two component contributions: the decrease of the Strouhal component magnitude associated with the progressive disappearance of the high-frequency force component, and simultaneously, the increase of the lock-in component magnitude, which dominates once the fully developed VIV regime is reached and the flow dynamics is entirely governed by wake–body synchronization.