Reconfiguration of elastic blades in oscillatory flow

Abstract

When subjected to a steady cross-flow, the deformation of flexible blades is known to result in the alleviation of the internal stresses in comparison to rigid structures. In the field of biomechanics, the flow-induced deformations of flexible structures leading to stress reduction have been often referred to as ‘reconfiguration’ in order to highlight the alleged benefits of such an adaptive process. In this paper, we investigate the reconfiguration of thin elastic blades and the resulting internal stresses when the flow about the blade is oscillatory. Our approach, based on numerical simulations using reduced order fluid force models, is validated by experimental observations. Through a systematic investigation of the response of the structure, we identify four kinematic regimes depending on the excursion of the fluid particles relative to the dimensions of the blade and on the frequency of the flow oscillations relative to the characteristic frequency of the blade. When the flow amplitude is smaller than the structural width, fluid inertia dominates over drag and the fluid–structure coupling triggers resonances that may cause a magnification of the internal stresses. But the small magnitude of the fluid load in this regime is unlikely to cause any severe damage in practice. Otherwise, when drag is the dominant load, flexibility always permits a reduction of the internal stresses. As in the static case, dynamic reconfiguration results in the concentration of the stresses within a small bending length whose scaling depends on the kinematic regime. The magnitude of the stresses does not depend on the actual length of the structure anymore, which suggests the absence of mechanical limitations to the axial growth of wave-swept plants. However, the risk of resonances originating from the inertial load when the blade width compares with the flow excursion favours elongated shapes that best accommodate the oscillatory fluid loadings.