Fluid-Structure Interaction Analysis of a Two-Dimensional Flag-in-Wind Problem by the ALE Finite Element Method

In a recent experiment, Zhang and co-workers found that a flexible filament in a flowing soap film can exhibit three states; stretched-straight, flapping, and bistability. When this experimental model is regarded as a one-dimensional flag in a two-dimensional fluid flow, their findings contradict the common idea that flags always flap in a wind. In this paper, the flag-in-wind problem is simulated by fluid-structure interaction finite element analysis where Navier-Stokes equations based on the ALE method are strongly coupled with Lagrangian equilibrium equations of the structure. In the simulation the three states are successfully reproduced, and the effects of some representative parameters on the amplitude and frequency of the oscillations are investigated to reveal the underlying mechanism involved in flag flapping.