On the wake and flapping dynamics of different aspect ratio flags

TL;DR

This study investigates how aspect ratio influences the flapping and wake dynamics of flags, revealing how aspect ratio affects wave propagation, vortex formation, and drag, with a new model predicting drag based on kinematic parameters.

Contribution

It provides systematic measurements and analysis of the impact of aspect ratio on flag flapping dynamics and introduces a kinematic model to predict mean drag coefficient without fitting.

Findings

Wave speed scales with flag length and aspect ratio.

Aspect ratio affects vortex shedding and circulation.

Drag coefficient varies widely with aspect ratio and mass ratio.

Abstract

The flapping of flags is a classical problem involving fast and large amplitude deformations of a thin flexible plate and unsteady flow phenomena. We perform systematic time and space-resolved measurements of the deformation and drag acting on flapping flags for various aspect ratios and mass ratios. Bending waves travel from the root to the tip at a speed close to the incoming flow and the typical wavelength of the waves scales with the length of the flag. With smaller aspect ratio, the local dynamic pressure exerted by the fluid on the flag is reduced, lowering the wave propagation speed, and reducing the tip frequency. The effect of aspect ratio on the vortex formation in the near wake is analysed using flow field measurements. We identified two characteristic length scales, the ratio of the flag area over its perimeter $L^*$ and the square root of area $\sqrt{HL}$ that scale the circulation shed during a cycle. Changes in aspect ratio and mass ratio generate a wide scattering of the mean drag coefficient, ranging from 0 to 0.55. We discuss a kinematic-based model for the mean drag coefficient. This model uses the mass ratio and the typical tip speed, which depends linearly on the wave speeds, to predict the mean drag coefficient without any fitting parameter.