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to reduce the drag, be flexible
(click on an image for a larger view)
Trees bend and tree leaves passively "fold up" in strong winds. Thanks to their flexibility, as a consequence, many terrestrial plants can survive because they are able to compromise to high-speed air flows. The reason is the following: if tree leaves were rigid, the aerodynamic drag exerted by the wind grows with the square of the wind speed. If the leaves deform under the forces applied onto them, however, the growth of drag increases at a much slower rate. The changing drag coefficient, a function of the area or/and shape, results in less drag that prevents possible damages to the leaves.

To study this phenomenon in a laboratory setting, we constructed a fast flowing quasi-2D water tunnel: a flowing soap film. Our 1D leave, a thin elastic glass fiber, is inserted transverse to the flow direction. With increased flow rate, the glass fiber is bent progressively while the flow passes by on both sides of the fiber. We then measure the flow speed with a Laser Doppler Velocimetry, measure the force applied onto the fiber and record its shapes. The outcome is compared with a numerical simulation (a 2D model that accounts for an ideal flow and the fiber's elasticity). We found that the power that relates force to the flow speed changes from 2 to 4/3, through a bulking-like transition from being straight to a nearly parabola.

To learn more details on this project, please read articles "Drag reduction through self-similar bending of a flexible body" that was published in Nature, 420, 479, 2002 and "How flexibility induces streamlining in a two-dimensional flow," published in Physics of Fluids, 16, 1694, 2004
Figure 1. A thin glass fiber of 10-200 micron thick is inserted transverse into a fast flowing soap film. A "Cavendish-type" setup is used to measure the small forces involved in this experiment. For details, please read the article.
Figure 2. Two photos on the left show how a thin glass fiber is bent progressively as the speed of the soap film is increased. A numeric solution (see article) on the right shows the streamlines and the pressure distribution around the flexible fiber.
Figure 3. Fibers are bent due to fluid forces: viscous force and pressure force. Shapes are compared between experimental observations and numeric simulations.
Figure 4. Scaling of forces both for rigid fiber and a flexible fiber, solid lines are predictions from the numerical model. Symbol "Eta" on the right bottom is a dimensionless number that incorporates the fluid force and the bending rigidity of the fiber.
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