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Drag reduction through self-similar bending of a flexible body

Abstract

The classical theory of high-speed flow1 predicts that a moving rigid object experiences a drag proportional to the square of its speed. However, this reasoning does not apply if the object in the flow is flexible, because its shape then becomes a function of its speed—for example, the rolling up of broad tree leaves in a stiff wind2. The reconfiguration of bodies by fluid forces is common in nature, and can result in a substantial drag reduction that is beneficial for many organisms3,4. Experimental studies of such flow–structure interactions5 generally lack a theoretical interpretation that unifies the body and flow mechanics. Here we use a flexible fibre immersed in a flowing soap film to measure the drag reduction that arises from bending of the fibre by the flow. Using a model that couples hydrodynamics to bending, we predict a reduced drag growth compared to the classical theory. The fibre undergoes a bending transition, producing shapes that are self-similar; for such configurations, the drag scales with the length of self-similarity, rather than the fibre profile width. These predictions are supported by our experimental data.

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Figure 1: The layout of the experiment. A glass fibre (F) is inserted into a flowing soap-film tunnel (partly shown).
Figure 2: Examples of the flow field and fibre shape in experiment and model.
Figure 3: Comparison of six experimental fibre shapes with model shapes.
Figure 4: Comparison of drag data from experiment and model.

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Acknowledgements

We thank F. Vollmer, S. Childress, A. Libchaber and P. Palffy-Muhoray for conversations, and Y.-Q. Xia who assisted in a preliminary experimental study of the fibre/flow system. M.S. thanks A. Goriely, who originally suggested this as an interesting problem. This work was supported by the National Science Foundation and the Department of Energy.

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Correspondence to Michael Shelley.

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Alben, S., Shelley, M. & Zhang, J. Drag reduction through self-similar bending of a flexible body. Nature 420, 479–481 (2002). https://doi.org/10.1038/nature01232

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