Dynamic interactions of multiple wall-mounted flexible flaps

Abstract

Coherent waving interactions between vegetation and fluid flows are known to emerge under conditions associated with the mixing layer instability. A similar waving motion has also been observed in flow control applications, where passive slender structures are used to augment bluff body wakes. While their existence is well reported, the mechanisms which govern this behaviour, and their dependence on structural properties, are not yet fully understood. This work investigates the coupled interactions of a large array of slender structures in an open-channel flow, via numerical simulation. A direct modelling approach, whereby the individual structures are fully resolved, is realised via a lattice Boltzmann-immersed boundary-finite element model. For steady flow conditions at low–moderate Reynolds number, the response of the array is measured over a range of mass ratio and bending rigidity, spanning two orders of magnitude, and the ensuing response is characterised. The results show a range of behaviours which are classified into distinct states: static, regular waving, irregular waving and flapping. The regular waving regime is found to occur when the natural frequency of the array approaches the estimated frequency of the mixing layer instability. Furthermore, after normalising with respect to the natural frequency of the array, the frequency response across the examined parameter space collapses onto a single curve. These findings indicate that the coherent waving mode is in fact a coupled instability, as opposed to a purely fluid-driven response, and that this specific regime is triggered by a lock-in between the fluid and structural natural frequencies.