Leclercq T, Peake N, de Langre E
Department of Mechanics, LadHyX, CNRS, École Polytechnique, 91128 Palaiseau, France.
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK.
Proc Math Phys Eng Sci. 2018 Jan;474(2209):20170678. doi: 10.1098/rspa.2017.0678. Epub 2018 Jan 3.
The static reconfiguration of flexible beams exposed to transverse flows is classically known to reduce the drag these structures have to withstand. But the more a structure bends, the more parallel to the flow it becomes, and flexible beams in axial flows are prone to a flutter instability that is responsible for large inertial forces that drastically increase their drag. It is, therefore, unclear whether flexibility would still alleviate, or on the contrary enhance, the drag when flapping occurs on a reconfiguring structure. In this article, we perform numerical simulations based on reduced-order models to demonstrate that the additional drag induced by the flapping motion is almost never significant enough to offset the drag reduction due to reconfiguration. Isolated and brief snapping events may transiently raise the drag above that of a rigid structure in the particular case of heavy, moderately slender beams. But apart from these short peak events, the drag force remains otherwise always significantly reduced in comparison with a rigid structure.
经典理论认为,暴露于横向流中的柔性梁进行静态重构可减少这些结构必须承受的阻力。但结构弯曲得越多,其与流动方向就越平行,而轴向流中的柔性梁容易出现颤振失稳,这会产生大幅增加其阻力的巨大惯性力。因此,当在重构结构上发生拍打时,柔性是否仍会减轻阻力,或者相反会增加阻力,尚不清楚。在本文中,我们基于降阶模型进行了数值模拟,以证明拍打运动引起的额外阻力几乎从未大到足以抵消重构导致的阻力降低。在重且适度细长梁的特殊情况下,孤立且短暂的突然折断事件可能会使阻力瞬间高于刚性结构的阻力。但除了这些短暂的峰值事件外,与刚性结构相比,阻力在其他情况下始终会显著降低。